49 research outputs found
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