Exactly solvable supersymmetric quantum mechanics. (English) Zbl 0731.47055

Summary: In an abstract framework, we present a class of supersymmetric quantum mechanics whose eigenvalue problem is (in part) exactly solvable. In concrete realizations, the class includes supersymmetric quantum mechanical models associated with one-dimensional or radial Schrödinger operators with potentials of a special type, called “shape-invariant potentials” in the physics literature.


81Q60 Supersymmetry and quantum mechanics
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
47N50 Applications of operator theory in the physical sciences
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