Tru Physics

Problem 4.2 – Griffith’s Intro to QM

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Problem 4.2

Use separation of variables in cartesian coordinates to solve the infinite cubical well (or “particle in a box”):

V(x,y,z) = \begin{cases} 0, & \text{x, y, z all between 0 and a} \\ \infty , \text{otherwise.} \end{cases}

(a) Find the stationary states, and the corresponding energies.

(b) Call the distinct energies E_1, E_2, E_3, ... , in order of increasing energy. Find E_1,E_2,E_3,E_4,E_5, and E_6. Determine their degeneracies (that is, the number of different states that share the same energy). Comment: In one dimension degenerate bound states do not occur (see Problem 2.44), but in three dimensions they are very common.

(c) What is the degeneracy of E_{14}, and why is this case interesting?

Solution:

Problem 4.2 - Griffith's Intro to QM 1 of 3
Problem 4.2 - Griffith's Intro to QM 2 of 3
Problem 4.2 - Griffith's Intro to QM 3 of 3

Problem 4.2 Solution (Download)

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