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Exact ground state of a solvable sextic potential

For

V (x) = \frac{ℏ ^{2}}{2 m} (x^{6} - 3 x^{2} + 2),

the nodeless wavefunction

e^{- x^{4} /4}

is an exact eigenstate with energy

ℏ^{2} / m

, and hence is the ground state.

 Ancestors (5)

 Incoming links (1)

Solution