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
Phase-integral treatment of the linear plus Coulomb potential. I. Energy levels: Bo Thidé and Staffan Linnaeus, Institute of Theoretical Physics, University of Uppsala, Thunbergsvägen 3, S-752 38 Uppsala, Sweden
- Publisher
- Elsevier Science
- Year
- 1985
- Tongue
- English
- Weight
- 65 KB
- Volume
- 164
- Category
- Article
- ISSN
- 0003-4916
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## Phase-Integral Treatment of the Linear Plus Coulomb Potential. ## I. Energy Levels Bo THID~ AND STAFFAN ## LINNAEUS The first-, third-. and fifth-order phase-integral quantization conditions for the radial potential V(r) = LII' ~ h/r are expressed explicitly in terms of complete elliptic
Phase-Integral Calculation of Quanta1 Matrix Elements of exp{ -ax} between Unbound States in the One-Dimensional Potential C exp{ -ax}.
Phase-Integral Calculation of Quanta1 Matrix Elements of exp{ -ax} between Unbound States in the One-Dimensional Potential C exp{ -ax}.
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