Question

For a particle in a three-dimensional cubical box, what is the degeneracy (number of different quantum states with the same energy) of the energy levels (a) 3$\pi$ $\hslash$$^2$/$2mL$$^2$ and (b) 9$\pi$$^2$$\hslash$$^2$/$2mL$$^2$?

Name: for a particle in a three dimensional cubical box what is the degeneracy number of different quantum states with the same energy of the energy levels a 3pi hslash22ml2 and b 9pi2hslash22ml2 2
Uploaded: 2021-08-09T02:33:52-08:00
Duration: 55 s
Channel: Manne Andergronde
Description: for a particle in a three dimensional cubical box what is the degeneracy number of different quantum states with the same energy of the energy levels a 3pi hslash22ml2 and b 9pi2hslash22ml2 2

          For a particle in a three-dimensional cubical box, what is the degeneracy (number of different quantum states with the same energy) of the energy levels (a) 3$\pi$ $\hslash$$^2$/$2mL$$^2$ and (b) 9$\pi$$^2$$\hslash$$^2$/$2mL$$^2$?

Added by Patrick W.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Chapter 41

Instant Answer

Solved by Expert Manne Andergronde

08/09/2021

Step 1

Step 1: Recall the formula for the energy levels of a particle in a three-dimensional box: $E_{n_x,n_y,n_z} = \frac{{\pi^2 \hbar^2}}{{2mL^2}}(n_x^2 + n_y^2 + n_z^2)$ Show more…

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For a particle in a three-dimensional cubical box, what is the degeneracy (number of different quantum states with the same energy) of the energy levels (a) 3$\pi$ $\hslash$$^2$/$2mL$$^2$ and (b) 9$\pi$$^2$$\hslash$$^2$/$2mL$$^2$?