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Phase-integral treatment of the linear plus Coulomb potential. II. Expectation values and the probability density at the origin: Staffan Linnaeus and Mats Düring, Institute of Theoretical Physics, University of Uppsala, Thunbergsvägen 3, S-752 38 Uppsala, Sweden

Publisher
Elsevier Science
Year
1985
Tongue
English
Weight
43 KB
Volume
164
Category
Article
ISSN
0003-4916

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✦ Synopsis

The linear plus Coulomb potential V(r) =ar-b/r is considered.

The first-, third, and fifth-order phase-integral formulas for expectation values of integer powers of r are expressed in terms of complete elliptic integrals. It is pointed out how these results can be used to calculate the probability density close to the origin.

📜 SIMILAR VOLUMES

Phase-integral treatment of the linear p
Phase-integral treatment of the linear plus Coulomb potential. II. Expectation values and the probability density at the origin
✍ Staffan Linnaeus; Mats Düring 📂 Article 📅 1985 🏛 Elsevier Science 🌐 English ⚖ 361 KB

The linear plus Coulomb potential V(r) = ar -b/r is considered. The first-, third-, and tilthorder phase-integral formulas for expectation values of integer powers of r are expressed in terms of complete elliptic integrals. It is pointed out how these results can be used to calculate the probabilit

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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}.

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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