Closed expressions for matrix elements of the trigonometric Pöschl-Teller potential. (English) Zbl 1238.81106
Summary: Analytical matrix elements of the \(x^n\) (\(n>0\)) and \([\tan(x)]^m[cos(x)]^{m'}d^nn/dx^n\) operators are derived using the eigenfunctions of the symmetric trigonometric Pöschl-Teller potential. The closed formulas are written in terms of Gauss hypergeometric functions and could be used in variational calculations to describe vibrational energy levels associated with bending modes. Multiprecision computational packages are considered in order to obtain an arbitrary level of precision.
MSC:
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 34L40 | Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) |
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
| 81V55 | Molecular physics |
Software:
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