The generalization of the Schrdinger equation to three dimensions is For a particle confined to the cubical

The generalization of the Schrödinger equation to three dimensions is

For a particle confined to the cubical region 0 ≤ x ≤ L, 0 ≤ y ≤ L, 0 ≤ z ≤ L, show by direct substitution that the equation is satisfied by wave functions of the form ψ (x, y, z) = A sin(n_xπx/L) sin(n_yπy/L) sin(n_zπz/L), where the n’s are integers and A is a constant. (b) In the process of working part (a), verify that the energies E are given by Equation 35.8.

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U(x, y, z)ự = Ey %3D 2m ax? ay? 2