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→The infinite potential well: In the following article it states, that subscript zero means: Zero is included. https://en.m.wikipedia.org/wiki/Natural_number Tags: Mobile edit Mobile web edit |
m whatever that Wikipedia article may claim, not the entire world uses that notation, and many use the opposite notation, get over it; let's use a notation that is unambiguous for everyone, shall we? |
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where ''A'' is the depth of the potential and ''L'' is the length of the well. We will compute this determinant by diagonalizing the operator and multiplying the [[eigenvalue]]s. So as not to have to bother with the uninteresting divergent constant, we will compute the quotient between the determinants of the operator with depth ''A'' and the operator with depth ''A'' = 0. The eigenvalues of this potential are equal to
:<math> \lambda_n = \frac{n^2\pi^2}{L^2} + A \qquad (n \in \mathbb N \setminus \{0\}). </math>
This means that
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