Phy5645/Problem 1D sample

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The Schrödinger equation takes the form,

Let us assume that has the form, Then


Dividing by we obtain

We may now separate the left-hand side into three parts, each depending on only one of the three coordinates and Each of these parts must be equal to a constant. Therefore,

where , and are constants and

Hence, the three-dimensional problem has been divided into three one-dimensional problems where the total energy is the sum of the energies and in each dimension.

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