𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Exact formulas and phase-integral formulas, not involving wavefunctions, for expectation values pertaining to general potentials

✍ Scribed by Nanny Fröman; Per Olof Fröman

Publisher
Elsevier Science
Year
1985
Tongue
English
Weight
674 KB
Volume
163
Category
Article
ISSN
0003-4916

No coin nor oath required. For personal study only.

✦ 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.

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 quanta1 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.

📜 SIMILAR VOLUMES

Calculation of expectation values and ma
Calculation of expectation values and matrix elements for symmetric double-well potentials. II. Investigation of the accuracy of phase-integral formulas: Rolf Paulsson, Institute of Theoretical Physics, University of Uppsala, Thunbergsvägen 3, S-752 38 Uppsala, Sweden
📂 Article 📅 1985 🏛 Elsevier Science 🌐 English ⚖ 77 KB

Phase-Integral Calculation of Quanta1 Matrix Elements of exp{ -ax} between Unbound States in the One-Dimensional Potential C exp{ -ax}.

Calculation of expectation values and ma
Calculation of expectation values and matrix elements for symmetric double-well potentials. I. General theory according to phase-integral method: Rolf Paulsson and Nanny Fröman, Institute of Theoretical Physics, University of Uppsala, Thunbergsvägen 3, S-752 38 Uppsala, Sweden
📂 Article 📅 1985 🏛 Elsevier Science 🌐 English ⚖ 77 KB

Phase-Integral Calculation of Quanta1 Matrix Elements of exp{ -ax} between Unbound States in the One-Dimensional Potential C exp{ -ax}.