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Exercise 10.2.1* (Particle in a Three-Dimensional Box). Recall that a particle in a one- dimensional box extending fromx=0 to L is confined to the region 0

Exercise 10.2.1* (Particle in a Three-Dimensional Box). Recall that a particle in a one- dimensional box extending fromx=0 to L is confined to the region 0

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Exercise 10.2.1* (Particle in a Three-Dimensional Box). Recall that a particle in a one- dimensional box extending fromx=0 to L is confined to the region 0<x<L; its wave function vanishes at the edges x=0 and L and beyond (Exercise 5.2.5). Consider now a particle confined in a three-dimensional cubic box of volume L’. Choosing as the origin one of its corners, and the x, y, and z axes along the three edges meeting there, show that the normalized energy eigenfunctions are (*) п,лу V E(x, y, z) =| sin L sin L sin L where hn? E= 2ML? (n+n + n²) and n; are positive integers.
Transcribed Image Text:Exercise 10.2.1* (Particle in a Three-Dimensional Box). Recall that a particle in a one- dimensional box extending fromx=0 to L is confined to the region 0<x<L; its wave function vanishes at the edges x=0 and L and beyond (Exercise 5.2.5). Consider now a particle confined in a three-dimensional cubic box of volume L’. Choosing as the origin one of its corners, and the x, y, and z axes along the three edges meeting there, show that the normalized energy eigenfunctions are (*) п,лу V E(x, y, z) =| sin L sin L sin L where hn? E= 2ML? (n+n + n²) and n; are positive integers.
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