THE EXPLICIT SOLUTIONS TO THE TIME-DEPENDENT SCHRÖDINGER EQUATIONS WITH THE SINGULAR POTENTIALS AND

DOI10.1081/PDE-100002238zbMath0983.35110OpenAlexW2026231494MaRDI QIDQ2747887

Shuji Watanabe

Publication date: 9 April 2002

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/pde-100002238

zbMATH Keywords

explicit solutionsinitial value problemtime-dependent Schrödinger equation

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) PDEs in connection with quantum mechanics (35Q40) Solutions to PDEs in closed form (35C05)

Related Items (5)

Calculation of the propagator of Schrödinger’s equation on (0, ∞) with the potential kx−2 + ω2x2 by Laplace’s method ⋮ EQUIVALENCE OF TIME-DEPENDENT SCHRÖDINGER EQUATIONS WITH CONSTANT AND TIME-DEPENDENT MASS ⋮ Hardy inequalities for functions vanishing at negligible sets and its applications ⋮ Semilinear Schrödinger evolution equations with inverse-square and harmonic potentials via pseudo-conformal symmetry ⋮ Form-preserving transformations for Hamiltonians with linear terms in the momentum

Cites Work

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• On the perturbation of linear operators in Banach and Hilbert spaces
• Three integrable Hamiltonian systems connected with isospectral deformations
• Über die Selbstadjungiertheit von Schrödinger-Operatoren
• Generalized Hermite polynomials and the heat equation for Dunkl operators
• Self-adjointness of the operators in Wigner’s commutation relations
• An uncertainty principle for Hankel transforms
• An embedding theorem of Sobolev type for an operator with singularity
• The explicit solution of a diffusion equation with singularity
• Do the Equations of Motion Determine the Quantum Mechanical Commutation Relations?
• A Note on the Quantum Rule of the Harmonic Oscillator

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