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Words: 27k
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Table of contents
27k
1k
Classical mechanics
Branch of physics
3k
156
Newtonian gravitational field
Classical mechanics
Degree of freedom
Classical mechanics
Mechanical constraint
Classical mechanics
Position
Classical mechanics
29
5
Plane polar coordinates
Position
Velocity
Position
3
Momentum
Classical mechanics
69
5
Rocket equation
Momentum
1
Angular momentum
Momentum
2
Energy
Classical mechanics
124
11
Work
Energy
2
Kinetic energy
Energy
1
Potential energy
Energy
4
Turning point
Energy
Period of an oscillation
Classical mechanics
Force
Classical mechanics
3
Newton's second law
Force
Newton's third law
Force
Normal force
Force
Circular motion
Classical mechanics
Inverse-square force
Classical mechanics
Displacement
Classical mechanics
Time
Classical mechanics
Mass
Classical mechanics
Rolling acceleration with rotational inertia
Classical mechanics
Angular momentum about the centre of mass
Classical mechanics
Legendre transform in mechanics
Classical mechanics
1
Singular Legendre transform of a degree-one velocity Lagrangian
Legendre transform in mechanics
Hamiltonian of a charged particle
Classical mechanics
Virial theorem
Classical mechanics
Hamiltonian mechanics
Classical mechanics
294
23
Phase space
Hamiltonian mechanics
1
Hamiltonian
Hamiltonian mechanics
1
Poisson bracket
Hamiltonian mechanics
26
4
Variational derivative
Hamiltonian mechanics
1
Canonical transformation
Hamiltonian mechanics
2
Integrable Hamiltonian system
Hamiltonian mechanics
94
7
Liouville theorem in Hamiltonian mechanics
Hamiltonian mechanics
Poincare recurrence theorem
Classical mechanics
Particle dynamics
Classical mechanics
103
10
One-dimensional conservative motion
Particle dynamics
34
4
Collision mechanics
Particle dynamics
3
Freely expanding rotating particle ring
Particle dynamics
Celestial mechanics
Classical mechanics
196
13
Kepler orbit
Celestial mechanics
60
12
Rigid body dynamics
Classical mechanics
408
23
Symmetric top
Rigid body dynamics
Angular velocity
Rigid body dynamics
Fixed space frame
Rigid body dynamics
Principal body frame
Rigid body dynamics
1
Euler equations for a torque-free rigid body
Rigid body dynamics
36
4
Moment of inertia
Rigid body dynamics
32
6
Euler angles for a symmetric top
Rigid body dynamics
64
4
Rolling without slipping
Rigid body dynamics
Lagrangian mechanics
Classical mechanics
511
28
Action
Lagrangian mechanics
1
Total-time-derivative invariance of a Lagrangian
Lagrangian mechanics
Charged-particle electromagnetic Lagrangian
Lagrangian mechanics
2
Generalized momentum
Lagrangian mechanics
1
Conserved quantities from cyclic coordinates
Lagrangian mechanics
Axially symmetric isotropic-mass Lagrangian
Lagrangian mechanics
Double pendulum
Lagrangian mechanics
2
Kinetic energy from Cartesian position vectors
Lagrangian mechanics
Small oscillation
Lagrangian mechanics
233
12
Conservation of energy from time-translation invariance
Lagrangian mechanics
Center of mass
Classical mechanics
141
6
Center-of-mass motion
Center of mass
124
4
Reduced mass
Center of mass
Uniform gravitational field
Classical mechanics
Normal coordinate
Classical mechanics
1
Antisymmetric molecular vibration
Normal coordinate
Continuum mechanics
Branch of physics
794
39
Material derivative
Continuum mechanics
34
3
Eulerian time average
Material derivative
Lagrangian trajectory
Material derivative
1
Rayleigh-Taylor instability
Continuum mechanics
Boundary layer
Continuum mechanics
38
4
Boundary-layer scaling
Boundary layer
Two-dimensional boundary-layer equations
Boundary layer
1
Boundary-layer separation
Boundary layer
Falkner-Skan equation
Continuum mechanics
Acoustic energy flux
Continuum mechanics
1
Transmitted velocity potential from a piston through an acoustic interface
Acoustic energy flux
Burgers vortex
Continuum mechanics
Elasticity
Continuum mechanics
545
24
Linear elasticity
Elasticity
166
12
Elastic-wave energy flux
Elasticity
162
10
Cosmology
Branch of physics
2k
100
Cosmological perfect-fluid continuity equation
Cosmology
45
3
Barotropic equation of state
Cosmological perfect-fluid continuity equation
22
2
Critical density
Cosmology
47
3
Cosmological density parameter
Critical density
21
2
Horizon problem
Cosmology
Radiation in cosmology
Cosmology
Cosmological constant energy
Cosmology
Big Crunch
Cosmology
Cosmic inflation
Cosmology
247
14
Inflaton
Cosmic inflation
97
5
Slow-roll approximation
Cosmic inflation
35
7
Linear cosmological density perturbation
Cosmology
128
12
Density contrast
Linear cosmological density perturbation
1
Jeans wavenumber
Linear cosmological density perturbation
Radiation domination
Linear cosmological density perturbation
Matter-era growing and decaying density modes
Linear cosmological density perturbation
2
Cosmological horizon crossing
Linear cosmological density perturbation
2
Cosmological density power spectrum
Linear cosmological density perturbation
1
Cosmological recombination
Cosmology
63
6
Saha ionization equation
Cosmological recombination
2
Free-electron fraction during hydrogen--helium recombination
Cosmological recombination
11
2
Friedmann equation
Cosmology
230
10
First integral of the Friedmann acceleration equation
Friedmann equation
Friedmann acceleration equation
Friedmann equation
32
5
Closed radiation--cosmological-constant turning polynomial
Friedmann equation
2
Phantom energy
Cosmology
Scale factor
Cosmology
95
7
Hubble parameter
Scale factor
1
Comoving coordinate
Scale factor
1
Cosmological redshift
Scale factor
2
Luminosity distance
Cosmology
1
Cosmological flux dimming
Luminosity distance
Friedmann-Lemaitre-Robertson-Walker metric
Cosmology
60
8
Milne universe
Friedmann-Lemaitre-Robertson-Walker metric
Spatially flat FLRW metric
Friedmann-Lemaitre-Robertson-Walker metric
Spatial curvature of an FLRW universe
Friedmann-Lemaitre-Robertson-Walker metric
Proper distance in cosmology
Friedmann-Lemaitre-Robertson-Walker metric
Conformal time
Friedmann-Lemaitre-Robertson-Walker metric
3
Cosmological continuity equation
Cosmology
42
4
Equation-of-state parameter
Cosmological continuity equation
31
3
Age of an FLRW universe
Cosmology
1
Hubble time
Age of an FLRW universe
Curvature-dominated universe
Cosmology
Deceleration parameter
Cosmology
1
Accelerating universe
Deceleration parameter
Big Bang nucleosynthesis
Cosmology
161
10
Neutron-proton chemical equilibrium
Big Bang nucleosynthesis
Cosmological weak freeze-out
Big Bang nucleosynthesis
1
Deuterium bottleneck
Big Bang nucleosynthesis
40
3
Primordial helium mass fraction
Big Bang nucleosynthesis
2
Baryon-to-photon ratio
Cosmology
Dynamical systems
Branch of physics
2k
89
Conservative planar phase portrait
Dynamical systems
Energy balance method
Dynamical systems
Relaxation oscillation
Dynamical systems
Discrete dynamical system
Dynamical systems
200
11
Iteration of a map
Discrete dynamical system
Interval map
Discrete dynamical system
119
6
Jury stability criterion
Discrete dynamical system
Multiplier of a periodic orbit of an iteration
Discrete dynamical system
Period-doubling bifurcation
Discrete dynamical system
Transcritical bifurcation
Dynamical systems
Center manifold
Dynamical systems
3
Center manifold of the 2024 Cambridge cubic system
Center manifold
Extended centre manifold of the 2023 Cambridge quadratic-product system
Center manifold
Bifurcations of the 2022 Cambridge quadratic-cubic system
Center manifold
Glendinning chaos
Dynamical systems
88
4
Horseshoe for an interval map
Glendinning chaos
1
Sharkovsky theorem
Glendinning chaos
1
Radially symmetric planar dynamical system
Dynamical systems
Devaney chaos
Dynamical systems
70
7
Topological transitivity
Devaney chaos
Dense periodic points
Devaney chaos
Sensitive dependence on initial conditions
Devaney chaos
Doubling map
Devaney chaos
23
3
Centre manifold theorem
Dynamical systems
2
Extended centre manifold for a parameter
Centre manifold theorem
Centre-manifold invariance equation
Centre manifold theorem
Bifurcation theory
Dynamical systems
152
13
Eigenvalue-crossing bifurcation test
Bifurcation theory
Saddle-node bifurcation
Bifurcation theory
Pitchfork bifurcation normal form
Bifurcation theory
2
Bifurcation diagram
Bifurcation theory
1
Hopf bifurcation
Bifurcation theory
1
Saddle-node bifurcation of periodic orbits
Bifurcation theory
Quintic radial Hopf equation
Bifurcation theory
Interior equilibrium branch connecting two boundary bifurcations
Bifurcation theory
1
Strict Lyapunov function
Dynamical systems
Stable manifold
Dynamical systems
Autonomous planar system
Dynamical systems
113
5
Equilibrium point of a dynamical system
Autonomous planar system
78
4
Bendixson-Dulac criterion
Dynamical systems
Omega-limit set
Dynamical systems
Periodic orbit
Dynamical systems
Poincare-Bendixson theorem
Dynamical systems
Floquet multiplier
Dynamical systems
1
Divergence test for a planar periodic orbit
Floquet multiplier
Fixed point stability for an autonomous differential equation
Dynamical systems
Fixed point stability for an iteration
Dynamical systems
Resonance
Dynamical systems
Unstable equilibrium
Dynamical systems
Equilibrium of an autonomous differential equation
Dynamical systems
26
2
Linear stability analysis
Equilibrium of an autonomous differential equation
1
Basin of attraction
Dynamical systems
Lyapunov function
Dynamical systems
145
11
Lyapunov stability
Lyapunov function
First Lyapunov theorem
Lyapunov function
Second Lyapunov theorem
Lyapunov function
Asymptotic stability
Lyapunov function
Ellipsoidal Lyapunov function
Lyapunov function
Invariant sublevel set
Lyapunov function
1
LaSalle invariance principle
Lyapunov function
86
3
Hyperbolic equilibrium
Dynamical systems
1
Linearization stability theorem
Hyperbolic equilibrium
Positively invariant set
Dynamical systems
1
Trapping region
Positively invariant set
Electromagnetism
Branch of physics
2k
116
Right-hand rule
Electromagnetism
Electric charge
Electromagnetism
77
9
Charge neutrality
Electric charge
Conservation of electric charge
Electric charge
Charge density
Electric charge
Electric current
Electric charge
19
5
Electric field
Electromagnetism
19
2
Electric potential
Electric field
1
Magnetic field
Electromagnetism
1
Magnetic flux
Magnetic field
Capacitance
Electromagnetism
1
Capacitance per unit length
Capacitance
Inductance
Electromagnetism
Bound charge and bound current
Electromagnetism
49
4
Electric polarization
Bound charge and bound current
1
Magnetization
Bound charge and bound current
1
Magnetic spherical-shell matching
Electromagnetism
Maxwell stress tensor
Electromagnetism
Proca equation
Electromagnetism
2
Lorenz constraint in Proca theory
Proca equation
Yukawa potential
Proca equation
Relativistic Lorentz force
Electromagnetism
28
3
Relativistic hyperbolic motion in a uniform electric field
Relativistic Lorentz force
Null crossed electromagnetic field
Relativistic Lorentz force
1
Charged particle in a uniform magnetic field
Electromagnetism
1
Damped cyclotron motion
Charged particle in a uniform magnetic field
Electrostatics
Electromagnetism
313
17
Coulomb's law
Electrostatics
Conductor in electrostatic equilibrium
Electrostatics
29
5
Electrostatic energy
Electrostatics
1
Electric dipole moment
Electrostatics
2
Electric multipole expansion
Electrostatics
62
4
Maxwell equations
Electromagnetism
54
10
Maxwell equations in matter
Maxwell equations
1
Ampère-Maxwell equation
Maxwell equations
Faraday's law
Maxwell equations
1
Gauss's law
Maxwell equations
Charge conservation from Maxwell equations
Maxwell equations
Covariant Maxwell equation with the minus-plus-plus-plus metric
Maxwell equations
Source-free Maxwell equations in a linear medium
Maxwell equations
1
Magnetic vector potential
Electromagnetism
81
7
Neumann's mutual-inductance formula
Magnetic vector potential
Coulomb gauge
Magnetic vector potential
Gauge transformation
Magnetic vector potential
Magnetic dipole moment
Magnetic vector potential
3
Biot-Savart law
Electromagnetism
2
On-axis magnetic field of a circular current loop
Biot-Savart law
Magnetic-field cancellation between oppositely driven coaxial loops
Biot-Savart law
Beltrami field
Electromagnetism
Relativistic electromagnetism
Electromagnetism
397
20
Relativistic charged-particle action
Relativistic electromagnetism
2
Electromagnetic four-potential
Relativistic electromagnetism
268
15
Lorentz transformation of electromagnetic fields
Relativistic electromagnetism
Electromagnetic wave
Electromagnetism
412
18
Electromagnetic wave equation
Electromagnetic wave
Plane electromagnetic wave
Electromagnetic wave
109
7
Poynting vector
Electromagnetic wave
49
3
Radiation zone
Electromagnetic wave
30
4
Fluid mechanics
Branch of physics
3k
135
Torricelli's law
Fluid mechanics
Mass density
Fluid mechanics
Fluid pressure
Fluid mechanics
Dynamic viscosity
Fluid mechanics
2
Kinematic viscosity
Dynamic viscosity
Reynolds number
Dynamic viscosity
Vorticity
Fluid mechanics
2
Circulation
Vorticity
Irrotational flow
Vorticity
Circular vortex-sheet mode
Fluid mechanics
Internal gravity wave
Fluid mechanics
3
Buoyancy frequency
Internal gravity wave
Vertical trapping of an internal gravity wave by planar strain
Internal gravity wave
Mountain-wave cutoff
Internal gravity wave
Stream function
Fluid mechanics
1
Streamline classification of a planar linear saddle or centre
Stream function
Streamline
Fluid mechanics
Velocity potential
Fluid mechanics
45
4
Potential flow around a circular cylinder
Velocity potential
Radially symmetric incompressible flow in a planar annulus
Velocity potential
28
2
Laminar plume
Fluid mechanics
18
3
Integral momentum-flux balance for a two-dimensional plume
Laminar plume
Similarity scaling of a two-dimensional laminar plume
Laminar plume
1
Euler equations for an inviscid fluid
Fluid mechanics
101
8
Unsteady Bernoulli equation
Euler equations for an inviscid fluid
Clebsch-potential variational derivation of incompressible Euler flow
Euler equations for an inviscid fluid
Bernoulli equation
Euler equations for an inviscid fluid
3
Integral momentum equation
Euler equations for an inviscid fluid
1
Conservation of mass in a pipe
Fluid mechanics
Viscous fluid flow
Fluid mechanics
1k
49
Viscous diffusion time
Viscous fluid flow
Couette flow
Viscous fluid flow
Falling film flow
Viscous fluid flow
1
Stress boundary condition
Viscous fluid flow
1
No-slip boundary condition
Viscous fluid flow
Newtonian fluid stress tensor
Viscous fluid flow
3
Navier-Stokes equation
Viscous fluid flow
1
Kinetic-energy balance for an incompressible Newtonian fluid
Viscous fluid flow
30
2
Stokes flow
Viscous fluid flow
178
18
Lubrication theory
Viscous fluid flow
174
11
Viscous shear torque
Viscous fluid flow
1
Body force
Fluid mechanics
Hydrostatic pressure
Fluid mechanics
Potential flow
Fluid mechanics
178
10
Potential flow around a translating sphere
Potential flow
Spherically symmetric incompressible radial flow
Potential flow
1
Squeezing wedge flow
Potential flow
Surface gravity wave
Potential flow
118
5
Streamfunction in polar coordinates
Fluid mechanics
Incompressible flow
Fluid mechanics
Streakline
Fluid mechanics
Kinematic boundary condition
Fluid mechanics
2
Kinematic boundary condition for a free-surface graph
Kinematic boundary condition
Linearized boundary condition
Kinematic boundary condition
Dynamic boundary condition for an inviscid interface
Fluid mechanics
1
Pressure continuity
Dynamic boundary condition for an inviscid interface
Wake (fluid dynamics)
Fluid mechanics
Shear layer
Fluid mechanics
41
2
Vortex sheet
Shear layer
1
Compressible flow
Fluid mechanics
182
8
Riemann invariant
Compressible flow
2
Normal shock wave
Compressible flow
29
4
Linear acoustics
Fluid mechanics
236
14
Homentropic pressure perturbation
Linear acoustics
Acoustic velocity potential
Linear acoustics
79
5
Acoustic energy conservation
Linear acoustics
Evanescent acoustic surface wave
Linear acoustics
22
3
Time average of harmonic power
Linear acoustics
1
General relativity
Branch of physics
1k
74
Plane-fronted gravitational wave
General relativity
Covariant derivative
General relativity
39
6
Tensor type
Covariant derivative
Parallel transport
Covariant derivative
1
Covariant derivative of a covariant tensor
Covariant derivative
Levi-Civita connection
Covariant derivative
1
Riemann curvature tensor
General relativity
227
15
Curvature commutator on a covariant tensor
Riemann curvature tensor
Symmetric Hessian of a scalar field
Riemann curvature tensor
First Bianchi identity
Riemann curvature tensor
Weyl tensor
Riemann curvature tensor
2
First-pair antisymmetry of the Riemann tensor
Riemann curvature tensor
Ricci tensor
Riemann curvature tensor
99
7
Normal coordinates
General relativity
Stress-energy tensor
General relativity
34
3
Conserved Klein-Gordon scalar stress-energy ansatz
Stress-energy tensor
Weak energy condition
Stress-energy tensor
1
Einstein field equations
General relativity
12
2
Trace-reversed Einstein field equations in D dimensions
Einstein field equations
1
Linearized gravity
General relativity
106
7
Trace-reversed metric perturbation
Linearized gravity
48
3
Linearized Ricci tensor and scalar
Linearized gravity
Newtonian limit of general relativity
Linearized gravity
1
Schwarzschild spacetime
General relativity
180
15
Radial Weyl curvature of Schwarzschild spacetime
Schwarzschild spacetime
1
Equatorial null orbit in Schwarzschild spacetime
Schwarzschild spacetime
1
Schwarzschild radius
Schwarzschild spacetime
Schwarzschild tortoise coordinate
Schwarzschild spacetime
34
2
Schwarzschild event horizon
Schwarzschild spacetime
Gravitational redshift between static Schwarzschild observers
Schwarzschild spacetime
Proper acceleration of a static Schwarzschild observer
Schwarzschild spacetime
Birkhoff theorem
Schwarzschild spacetime
1
Schwarzschild light deflection
Schwarzschild spacetime
1
Nordstrom theory of gravitation
General relativity
2
Conformally flat metric
Nordstrom theory of gravitation
Geodesic equation for a conformally flat metric
Nordstrom theory of gravitation
Anti-de Sitter spacetime
General relativity
47
3
Static coordinates on anti-de Sitter spacetime
Anti-de Sitter spacetime
2
Planarity of geodesics in spherical symmetry
General relativity
Timelike geodesic effective potential
General relativity
23
3
Effective-potential stability of a circular orbit
Timelike geodesic effective potential
Effective potential for timelike Schwarzschild geodesics
Timelike geodesic effective potential
1
Metric tensor
General relativity
1
Inverse metric
Metric tensor
Two-dimensional hyperbolic metric in polar coordinates
General relativity
2
Coordinate geodesics of the hyperbolic polar metric
Two-dimensional hyperbolic metric in polar coordinates
Curvature of the two-dimensional hyperbolic polar metric
Two-dimensional hyperbolic metric in polar coordinates
Ricci scalar
General relativity
Integrable systems
Branch of physics
533
33
Sinh-Gordon equation
Integrable systems
Sine-Gordon equation
Integrable systems
2
One-soliton solution of the sine-Gordon equation in light-cone coordinates
Sine-Gordon equation
Sine-Gordon breather
Sine-Gordon equation
Focusing nonlinear Schrodinger equation
Integrable systems
1
Bright standing soliton of the focusing nonlinear Schrodinger equation
Focusing nonlinear Schrodinger equation
Hamiltonian form of the cubic nonlinear Schrodinger equations
Integrable systems
Defocusing nonlinear Schrödinger equation
Integrable systems
2
No rapidly decaying standing wave for the defocusing cubic nonlinear Schrodinger equation
Defocusing nonlinear Schrödinger equation
Dark soliton
Defocusing nonlinear Schrödinger equation
Korteweg-De Vries equation
Integrable systems
46
4
KdV Schrodinger spectral problem
Korteweg-De Vries equation
16
2
Soliton
Korteweg-De Vries equation
Inverse scattering transform
Integrable systems
32
3
Discrete scattering data
Inverse scattering transform
Gelfand-Levitan-Marchenko equation
Inverse scattering transform
1
Poisson-commuting separated energies
Integrable systems
Separable forced harmonic oscillators
Integrable systems
Action variable of a shifted harmonic oscillator
Integrable systems
1
Phase-plane area formula for an action variable
Action variable of a shifted harmonic oscillator
Compatibility condition for an overdetermined linear system
Integrable systems
Lax pair
Integrable systems
63
7
Airy equation
Lax pair
AKNS Lax pair for the nonlinear Schrodinger equation
Lax pair
Isospectral Lax equation
Lax pair
2
Zero-curvature condition
Lax pair
Global relation for the half-line free Schrodinger equation
Lax pair
Tzitzeica equation
Integrable systems
Mathematical biology
Branch of physics
755
40
Per capita
Mathematical biology
Age-structured population model
Mathematical biology
1
Euler-Lotka equation
Age-structured population model
Law of mass action
Mathematical biology
Enzyme kinetics
Mathematical biology
29
3
Michaelis-Menten equation
Enzyme kinetics
Quasi-steady-state approximation
Enzyme kinetics
1
Autocatalysis
Mathematical biology
39
3
Autocatalytic biochemical switch
Autocatalysis
13
2
Cubic saturation population model
Mathematical biology
Exponential density-dependent birth model
Mathematical biology
Survival-augmented Ricker map
Mathematical biology
1
Stability interval of the survival-augmented Ricker equilibrium
Survival-augmented Ricker map
Malthusian delay differential equation
Mathematical biology
20
3
Method of steps for a delay differential equation
Malthusian delay differential equation
Characteristic equation of a delay differential equation
Malthusian delay differential equation
1
Epidemic threshold
Mathematical biology
Kramers-Moyal expansion
Mathematical biology
2
Constant-birth pair-annihilation process
Kramers-Moyal expansion
Kramers-Moyal master equation
Kramers-Moyal expansion
Compartmental model
Mathematical biology
199
15
Mass-action interaction
Compartmental model
Spatial SIR model
Compartmental model
2
Disease-free equilibrium
Compartmental model
Endemic equilibrium
Compartmental model
Susceptible-infective model with exponential density-dependent birth
Compartmental model
2
Basic reproduction number
Compartmental model
1
SIR model with demography and permanent immunity
Compartmental model
1
SIR model with waning immunity
Compartmental model
1
Quantum mechanics
Branch of physics
3k
156
Parity
Quantum mechanics
1
Spatial reflection
Parity
Photon
Quantum mechanics
Ground state
Quantum mechanics
Energy eigenvalue
Quantum mechanics
35
6
Energy eigenstate
Energy eigenvalue
Energy eigenspace
Energy eigenvalue
Excited state
Energy eigenvalue
1
Eigenstate
Energy eigenvalue
1
Quantum state
Quantum mechanics
224
15
Qubit state
Quantum state
Quantum number
Quantum state
Quantum phase
Quantum state
Observable
Quantum state
194
9
Bound state
Quantum state
Stationary state
Quantum state
Planck constant
Quantum mechanics
Wavefunction
Quantum mechanics
142
12
Plane wave
Wavefunction
Probability amplitude
Wavefunction
80
4
Normalizable wavefunction
Wavefunction
Probability density
Wavefunction
Probability current
Wavefunction
24
2
Gaussian wave packet
Wavefunction
Potential barrier
Quantum mechanics
40
2
Quantum tunnelling
Potential barrier
1
Hermitian operator on a nonorthogonal two-state basis
Quantum mechanics
1
Commuting time-dependent two-state Hamiltonian
Hermitian operator on a nonorthogonal two-state basis
Second moments of a complex Gaussian wave packet
Quantum mechanics
Finite square well
Quantum mechanics
Delta potential
Quantum mechanics
3
Bound state in a delta potential
Delta potential
Multiple delta potential
Delta potential
Scattering by a delta potential
Delta potential
Quantum scattering
Quantum mechanics
514
26
Reflected wave
Quantum scattering
Transmission probability
Quantum scattering
One-dimensional S-matrix
Quantum scattering
1
Partial-wave S-matrix
Quantum scattering
4
Lippmann-Schwinger equation
Quantum scattering
Scattering amplitude
Quantum scattering
254
15
Supersymmetric quantum mechanics
Quantum mechanics
36
3
Partner Hamiltonians
Supersymmetric quantum mechanics
Pöschl-Teller potential
Supersymmetric quantum mechanics
1
Reflectionless potential
Quantum mechanics
Position operator
Quantum mechanics
Momentum operator
Quantum mechanics
1
Canonical commutation relation
Momentum operator
Ehrenfest theorem
Quantum mechanics
3
Proof of Ehrenfest theorem from the Schrodinger equation
Ehrenfest theorem
Classical equations from Ehrenfest theorem
Ehrenfest theorem
Correspondence principle
Ehrenfest theorem
Angular momentum operator
Quantum mechanics
268
15
Addition of angular momentum
Angular momentum operator
22
5
Spin angular momentum
Angular momentum operator
47
8
Infinite square well
Quantum mechanics
1
Particle in a rectangular box
Infinite square well
Quantum degeneracy
Quantum mechanics
Orbital angular momentum
Quantum mechanics
43
8
Rotation commutators for orbital angular momentum
Orbital angular momentum
Orbital angular momentum commutation relations
Orbital angular momentum
Angular momentum ladder operator
Orbital angular momentum
Squared orbital angular momentum in position and momentum operators
Orbital angular momentum
1
Angular momentum ladder variable
Orbital angular momentum
1
Rotational invariance of a central-potential Hamiltonian
Orbital angular momentum
Quantum harmonic oscillator
Quantum mechanics
45
4
Creation and annihilation operators
Quantum harmonic oscillator
30
2
Two commensurate quantum harmonic oscillators
Quantum harmonic oscillator
Three-dimensional isotropic harmonic oscillator
Quantum mechanics
Two-dimensional isotropic harmonic oscillator
Quantum mechanics
2
Oscillator bilinear commutator
Two-dimensional isotropic harmonic oscillator
Schwinger boson representation
Two-dimensional isotropic harmonic oscillator
Fermi oscillator
Quantum mechanics
2
Projection Hamiltonian
Fermi oscillator
Fermionic raising and lowering operator
Fermi oscillator
Tensor product of quantum systems
Quantum mechanics
192
11
Multiparticle quantum state
Tensor product of quantum systems
169
7
Decoupled Fermi oscillators
Tensor product of quantum systems
Kronecker product representation of local operators
Tensor product of quantum systems
Decoupled commuting Hamiltonian terms
Tensor product of quantum systems
Time-dependent perturbation theory
Quantum mechanics
1
Continuum transition probability at long times
Time-dependent perturbation theory
Time-independent perturbation theory
Quantum mechanics
5
First-order energy correction
Time-independent perturbation theory
Nondegenerate energy eigenvalue
Time-independent perturbation theory
First-order nondegenerate perturbation theory
Time-independent perturbation theory
Second-order nondegenerate perturbation theory
Time-independent perturbation theory
Imaginary-coupled two-level Hamiltonian
Time-independent perturbation theory
Degenerate perturbation theory
Quantum mechanics
39
3
Perturbation diagonal within a degenerate eigenspace
Degenerate perturbation theory
Exact diagonalization within a degenerate subspace
Degenerate perturbation theory
1
Pauli X eigenstate
Quantum mechanics
Quantum theory
Branch of physics
3k
139
Gauge covariance of the Schrödinger equation
Quantum theory
Quantum measurement
Quantum theory
Amplitude amplification
Quantum theory
Density operator
Quantum theory
79
6
Von Neumann entropy
Density operator
1
Purity of a density operator
Density operator
Reduced density operator of a weakly coupled oscillator pair
Density operator
Bloch vector
Density operator
1
Quantum no-signalling
Quantum theory
Quantum cloning
Quantum theory
3
No-cloning theorem for two pure states
Quantum cloning
Clone-assisted asymptotic state discrimination
Quantum cloning
Perfect discrimination implies cloning for a known state family
Quantum cloning
Environment-assisted two-state pure-state transformation
Quantum theory
Helstrom-Holevo bound
Quantum theory
19
3
Helstrom measurement for two pure states
Helstrom-Holevo bound
1
Perfect distinguishability of pure states
Helstrom-Holevo bound
Unitary gate discrimination
Quantum theory
67
8
Single-use perfect discrimination of two unitary gates
Unitary gate discrimination
Numerical range
Unitary gate discrimination
1
Unit-circle spectrum of a unitary operator
Unitary gate discrimination
Spectral arc length of a unitary operator
Unitary gate discrimination
13
3
Robertson uncertainty principle
Quantum theory
2
Quadratic-norm proof of the Heisenberg uncertainty relation
Robertson uncertainty principle
Equality case of the Heisenberg uncertainty relation
Robertson uncertainty principle
Gaussian eigenstate for a quadratic potential
Quantum theory
Coherent state
Quantum theory
Born approximation
Quantum theory
Toffoli gate
Quantum theory
Boolean quantum oracle
Quantum theory
97
5
Quantum phase kickback
Boolean quantum oracle
53
3
Compute-phase-uncompute construction
Boolean quantum oracle
Quantum circuit
Quantum theory
Grover search algorithm
Quantum theory
42
4
Grover diffusion operator
Grover search algorithm
1
Grover rotation angle
Grover search algorithm
1
Quantum measurement in the computational basis
Quantum theory
Deutsch-Jozsa algorithm
Quantum theory
1
Deutsch-Jozsa test with an arbitrary uniform-state unitary
Deutsch-Jozsa algorithm
Quantum Fourier transform
Quantum theory
120
7
Square of the quantum Fourier transform
Quantum Fourier transform
Quantum Fourier transform of a periodic coset state
Quantum Fourier transform
Quantum period finding
Quantum Fourier transform
77
2
Cyclic shift diagonalization by the quantum Fourier transform
Quantum Fourier transform
Exact quantum phase estimation
Quantum Fourier transform
BB84 protocol
Quantum theory
Breidbart basis
Quantum theory
Bell state
Quantum theory
229
12
Reduced density matrix
Bell state
39
5
Local operations and classical communication
Bell state
56
4
Quantum dense coding
Bell state
Variational method
Quantum theory
44
8
Nodeless theorem for a one-dimensional ground state
Variational method
Exact ground state of a solvable sextic potential
Variational method
Gaussian variational estimate for a solvable sextic potential
Variational method
Ground-state energy monotonicity under potential ordering
Variational method
Quantum virial identity from scaling
Variational method
1
Exact variational solution in a two-level system
Variational method
1
Landau level
Quantum theory
73
11
Magnetic minimal coupling
Landau level
Cyclotron frequency
Landau level
Landau gauge
Landau level
Degeneracy of a Landau level
Landau level
Spin splitting of Landau levels
Landau level
Landau levels in crossed electric and magnetic fields
Landau level
Symmetric gauge
Landau level
59
4
Bloch theorem
Quantum theory
139
12
Periodic potential
Bloch theorem
Energy band
Bloch theorem
Nearly-free electron model
Bloch theorem
1
Floquet matrix for a one-dimensional periodic potential
Bloch theorem
1
Kronig-Penney model
Bloch theorem
2
Tight-binding model
Bloch theorem
1
Brillouin zone
Bloch theorem
Hadamard gate
Quantum theory
Pauli Z gate
Quantum theory
Pauli X gate
Quantum theory
Inverse quantum circuit
Quantum theory
Controlled unitary gate
Quantum theory
179
11
Controlled-NOT gate
Controlled unitary gate
130
6
Hadamard test
Controlled unitary gate
2
Swap test
Controlled unitary gate
Parallel quantum gates
Quantum theory
Measurement of a Pauli observable
Quantum theory
Born rule for a product-basis measurement
Quantum theory
2
Matching-outcome projector
Born rule for a product-basis measurement
Product-state factorization of measurement probabilities
Born rule for a product-basis measurement
Maximally entangled state
Quantum theory
2
Orthogonal-basis invariance of a real Bell state
Maximally entangled state
Bell-state correlation in two real bases
Maximally entangled state
Shor algorithm
Quantum theory
87
6
Factor extraction from an even modular order
Shor algorithm
Quantum order finding
Shor algorithm
45
4
Special relativity
Branch of physics
284
29
Lorentz factor
Special relativity
Ultrarelativistic particle
Special relativity
Galilean transformation
Special relativity
Lorentz transformation
Special relativity
2
Nonrelativistic limit
Lorentz transformation
Relativistic velocity-addition formula
Lorentz transformation
Four-vector
Special relativity
Causality
Special relativity
Minkowski spacetime
Special relativity
84
6
Minkowski metric
Minkowski spacetime
31
5
Subluminal speed
Special relativity
Impossibility of photon decay into two massive particles
Special relativity
Four-momentum
Special relativity
71
7
Relativistic energy-momentum relation
Four-momentum
2
Relativistic force
Four-momentum
1
Relativistic two-body decay
Four-momentum
Mandelstam variables
Four-momentum
Four-velocity
Special relativity
Four-acceleration
Special relativity
17
2
Proper acceleration
Four-acceleration
1
Statistical physics
Branch of physics
2k
120
One-dimensional freely jointed chain
Statistical physics
22
2
Fixed-tension partition function of a one-dimensional chain
One-dimensional freely jointed chain
1
State degeneracy
Statistical physics
3
Degeneracy factor
State degeneracy
Microstate
State degeneracy
Macrostate
State degeneracy
Quantum ideal-gas statistics
Statistical physics
509
25
Maxwell-Boltzmann distribution
Quantum ideal-gas statistics
Bose-Einstein distribution
Quantum ideal-gas statistics
133
8
Density of states
Quantum ideal-gas statistics
Fermi-Dirac distribution
Quantum ideal-gas statistics
302
11
Classical limit of Bose--Einstein and Fermi--Dirac statistics
Quantum ideal-gas statistics
1
Planck photon distribution
Statistical physics
1
Temperature scaling of thermal photon number and energy densities
Planck photon distribution
Thermodynamics
Statistical physics
625
53
Boltzmann constant
Thermodynamics
Temperature
Thermodynamics
Thermal equilibrium
Thermodynamics
Entropy
Thermodynamics
Second law of thermodynamics
Thermodynamics
35
4
Heat
Thermodynamics
36
3
Third law of thermodynamics
Thermodynamics
Pressure
Thermodynamics
37
3
Volume
Thermodynamics
Internal energy
Thermodynamics
Free energy
Thermodynamics
Chemical potential
Thermodynamics
16
2
Ideal gas
Thermodynamics
4
Dieterici equation
Thermodynamics
Intensive and extensive thermodynamic quantities
Thermodynamics
Euler theorem for homogeneous functions
Thermodynamics
1
Gibbs free energy
Thermodynamics
81
5
Thermodynamic conjugate variable
Thermodynamics
First law of thermodynamics
Thermodynamics
24
2
Enthalpy
Thermodynamics
2
Diatomic ideal-gas enthalpy
Thermodynamics
Irreversible adiabatic piston compression
Thermodynamics
Constant-pressure heating of an ideal gas
Thermodynamics
Thermodynamic cycle
Thermodynamics
3
Gibbs entropy
Statistical physics
1
Maximum-entropy derivation of equilibrium ensembles
Gibbs entropy
Microcanonical ensemble
Statistical physics
Grand canonical ensemble
Statistical physics
2
Grand canonical partition function
Grand canonical ensemble
Grand potential
Grand canonical ensemble
Equivalence of statistical ensembles
Statistical physics
Canonical ensemble
Statistical physics
281
18
Canonical partition function
Canonical ensemble
124
9
Spin-1 paramagnet
Canonical ensemble
1
Negative temperature
Canonical ensemble
2
Equipartition theorem
Canonical ensemble
Nonrelativistic equilibrium number density
Canonical ensemble
Boltzmann factor
Canonical ensemble
Ideal-gas atmosphere in uniform gravity
Statistical physics
13
3
Barometric formula
Ideal-gas atmosphere in uniform gravity
1
Hydrostatic equilibrium
Ideal-gas atmosphere in uniform gravity
Ideal gas free energy
Statistical physics
Ancestors
(2)
Physics
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