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Numerical computation of an integral appearing in the Fröman-Fröman phase-integral formula for calculation of quantal matrix elements without the use of wave functions

✍ Scribed by Sven-Åke Gustafson; Staffan Lindahl

Publisher
Elsevier Science
Year
1977
Tongue
English
Weight
619 KB
Volume
24
Category
Article
ISSN
0021-9991

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✍ P.O Fröman; A Hökback; E Walles; S Yngve 📂 Article 📅 1985 🏛 Elsevier Science 🌐 English ⚖ 551 KB

In order to obtain further information on the accuracy of phase-integral formulas for calculating quanta1 expectation values and matrix elements involving unbound states, without the use of wavefunctions, the formulas are applied to an exactly soluble one-dimensional model. In this model the potenti

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Phase-integral calculation of quantal matrix elements of exp{−ax} between unbound states in the one-dimensional potential C exp{−ax}: P. O. Fröman, A. Hökback, E. Walles, and S. Yngve, Institute of Theoretical Physics, University of Uppsala, Thunbergsvägen 3, S-752 38 Uppsala, Sweden
📂 Article 📅 1985 🏛 Elsevier Science 🌐 English ⚖ 125 KB

An exact formula for quanta1 expectation values associated with bound states in a general potential is derived. The formula does not contain wavefunctions, but is expressed in terms of derivatives, with respect to an auxiliary parameter and with respect to the energy, of a function appearing in an e