OurBigBook.comSite Source code

Magnetic translation operator

For a lattice vector

r

,

T_{r} = exp (\frac{i}{ℏ} r \cdot K)

acts in the symmetric gauge as

(T_{r} ψ) (x) = exp (\frac{i e}{2ℏ} r \cdot (B \times x)) ψ (x + r) .

It commutes with

(p - e A)^{2} / (2 m) + V (x)

when

V (x + r) = V (x)

.

Table of contents 59 2
- Magnetic translation algebra Magnetic translation operator 31 1
  - Magnetic flux quantum Magnetic translation algebra 18

 Ancestors (7)

 Incoming links (1)

Solution