Wilson-Sommerfeld quantization rules

[th5418]

Homework Statement

Use the Wilson-Sommerfeld quantization rules to obtain the energy levels of a perfectly elastic particle of mass m in a cubic box of edge a in terms of the quantum numbers $$n_x, n_y, n_z$$

Homework Equations

$$\oint pdq = nh$$
Where p is a momentum, and dq is the corresponding coordinate system.

The Attempt at a Solution

Am I suppose to solve schrodinger's equation for particle in a box? That's the only way I know how...

 

[Jhero]

Hello there! Yes, to obtain the energy levels of a perfectly elastic particle in a cubic box using the Wilson-Sommerfeld quantization rules, you will need to solve the Schrodinger's equation for a particle in a box. This equation takes into account the wave nature of the particle and gives a more accurate description of its energy levels. The Wilson-Sommerfeld quantization rules state that the integral of momentum over a closed loop in phase space is quantized in units of h (Planck's constant). In this case, the closed loop is defined by the boundaries of the cubic box, and the momentum is given by the wave function of the particle. By solving the Schrodinger's equation and applying the quantization rules, you will be able to obtain the energy levels in terms of the quantum numbers n_x, n_y, n_z. Hope this helps!