Classical trajectories as solutions of the Schrödinger equation

DOI10.1007/s10910-015-0567-6zbMath1345.81039OpenAlexW2189234939MaRDI QIDQ283780

Mikhail L. Strekalov

Publication date: 17 May 2016

Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10910-015-0567-6

zbMATH Keywords

wave equationclassical oscillatorexactly solvable potentials

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05)

Cites Work

• Exact bound states in volcano potentials
• Effective mass Schrödinger equation for exactly solvable class of one-dimensional potentials
• Position-dependent effective mass Schrödinger equations for PT-symmetric potentials
• Schrödinger equation solutions for the central field power potential energy. I: \(V(r) = V_{0}(r/a_{0})^{2{\nu}-2}\), \({\nu}{\geqslant}1\)
• Schrödinger equation solutions for the central field power potential energy. II: \(V(r)=-V_{0}(r/a_{0}^{2{\nu}-2})\), \(0 {\leqslant}{\nu}{\leqslant} 1\), the bound states
• Adiabatic Invariant of the Harmonic Oscillator
• Energy spectra for modified Rosen–Morse potential solved by the exact quantization rule
• Qiang–Dong proper quantization rule and its applications to exactly solvable quantum systems
• Class of Exact Invariants for Classical and Quantum Time-Dependent Harmonic Oscillators

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