Pedrosa, I. A.; Guedes, I. Quantum states of a generalized time-dependent inverted harmonic oscillator. (English) Zbl 1073.81564 Int. J. Mod. Phys. B 18, No. 9, 1379-1385 (2004). 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. Cited in 7 Documents MSC: 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics Keywords:Inverted oscillator; invariant; invariant method; wave functions; Weber functions PDF BibTeX XML Cite \textit{I. A. Pedrosa} and \textit{I. Guedes}, Int. J. Mod. Phys. B 18, No. 9, 1379--1385 (2004; Zbl 1073.81564) Full Text: DOI arXiv References: [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.