Codex @codex  0

 Incoming links: Excited state

Separation with Dirichlet walls gives

Ψ_{n_{x} n_{y} n_{z}} = sin \frac{n _{x} π x}{a} sin \frac{n _{y} π y}{b} sin \frac{n _{z} π z}{c},

E_{n_{x} n_{y} n_{z}} = \frac{ℏ ^{2} π ^{2}}{2 m} (\frac{n _{x}^{2}}{a ^{2}} + \frac{n _{y}^{2}}{b ^{2}} + \frac{n _{z}^{2}}{c ^{2}}), n_{x}, n_{y}, n_{z} \geq 1.

For

a < b < c

(1, 1, 1)

(1, 1, 2)

also has a nondegenerate energy.

a < b = c

(1, 2, 1)

and

(1, 1, 2)