Quantum states of a generalized time-dependent inverted harmonic oscillator. (English) Zbl 1073.81564

Summary: We discuss the extension of the Lewis and Riesenfeld method of solving the time-dependent Schrödinger equation to cases where the invariant has continuous eigenvalues and apply it to the case of a generalized time-dependent inverted harmonic oscillator. As a special case, we consider a generalized inverted oscillator with constant frequency and exponentially increasing mass.


81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
Full Text: DOI arXiv


[1] DOI: 10.1007/BF02728488
[2] DOI: 10.1088/0305-4470/27/6/039 · Zbl 0838.35104
[3] DOI: 10.1142/S0217984902004147 · Zbl 1081.81519
[4] DOI: 10.1063/1.1664991
[5] DOI: 10.1103/PhysRevA.25.2388
[6] DOI: 10.1016/0003-4916(86)90142-9
[7] Abramowitz M., Handbook Mathematical Functions (1970)
[8] Hartley J. G., Phys. Rev. A 24 pp 2837–
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.