Propagators of Generalized Schrödinger Equations Related by First-order Supersymmetry

We construct an explicit relation between propagators of generalized Schrödinger equations that are linked by a first-order supersymmetric transformation. Our findings extend and complement recent results on the conventional case [1]

Curvature induced toroidal bound states

Curvature induced bound state (E < 0) eigenvalues and eigenfunctions for a particle constrained to move on the surface of a torus are calculated. A limit on the number of bound states a torus with minor radius a and major radius R can support is obtained. A condition for mapping constrained particle wave functions on the torus into free particle wave functions is established.Comment: 6 pages, no figures, Late

Infinite square-well, trigonometric P\"oschl-Teller and other potential wells with a moving barrier

Using mainly two techniques, a point transformation and a time dependent supersymmetry, we construct in sequence several quantum infinite potential wells with a moving barrier. We depart from the well known system of a one-dimensional particle in a box. With a point transformation, an infinite square-well potential with a moving barrier is generated. Using time dependent supersymmetry, the latter leads to a trigonometric P\"oschl-Teller potential with a moving barrier. Finally, a confluent time dependent supersymmetry transformation is implemented to generate new infinite potential wells, all of them with a moving barrier. For all systems, solutions of the corresponding time dependent Schr\"odinger equation fulfilling boundary conditions are presented in a closed form

Nonlinear Supersymmetry as a Hidden Symmetry

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