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

• Publisher: Elsevier Science
• Year: 1985
• Tongue: English
• Weight: 125 KB
• Volume: 163
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(85)90359-8

✦ Synopsis

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 exact quantization condition. By replacing the exact quantization condition by a phase-integral quantization condition (which in some cases may be exact as well), one obtains a useful formula for calculating quantal expectation values, without the use of wavefunctions, for any potential for which a phase-integral quantization condition is known. Explicit phase-integral formulas are given for the case of a single-well potential. Calculation of Expectation Values and Mairix Elements for Symmetric Double-Well Potentials. I. General Theory According to Phase-Integral Method. ROLF PAULSSON AND NANNY FR~MAN, Phase-Integral Calculation of Quanta1 Matrix Elements of exp{ -ax} between Unbound States in the One-Dimensional Potential C exp{ -ax}.