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m Typo fixing, replaced: an Harmonic oscillator → a Harmonic oscillator, as in the linked article. |
→The infinite potential well: n=0 is no eigenvalue, the corresponding „eigenstate“ would be the null vector Tags: Mobile edit Mobile web edit |
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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
This means that
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