14 research outputs found
Supersymmetric Quantum Mechanics and Solvable Models
We review solvable models within the framework of supersymmetric quantum mechanics (SUSYQM). In SUSYQM, the shape invariance condition insures solvability of quantum mechanical problems. We review shape invariance and its connection to a consequent potential algebra. The additive shape invariance condition is specified by a difference-differential equation; we show that this equation is equivalent to an infinite set of partial differential equations. Solving these equations, we show that the known list of h-independent superpotentials is complete. We then describe how these equations could be extended to include superpotentials that do depend on h
Generation of a Novel Exactly Solvable Potential
We report a new shape invariant (SI) isospectral extension of the Morse
potential. Previous investigations have shown that the list of "conventional"
SI superpotentials that do not depend explicitly on Planck's constant
is complete. Additionally, a set of "extended" superpotentials has been
identified, each containing a conventional superpotential as a kernel and
additional -dependent terms. We use the partial differential equations
satisfied by all SI superpotentials to find a SI extension of Morse with novel
properties. It has the same eigenenergies as Morse but different asymptotic
limits, and does not conform to the standard generating structure for
isospectral deformations.Comment: 9 pages, 3 figure
Algebraic Description of Shape Invariance Revisited
We revisit the algebraic description of shape invariance method in
one-dimensional quantum mechanics. In this note we focus on four particular
examples: the Kepler problem in flat space, the Kepler problem in spherical
space, the Kepler problem in hyperbolic space, and the Rosen-Morse potential
problem. Following the prescription given by Gangopadhyaya et al., we first
introduce certain nonlinear algebraic systems. We then show that, if the model
parameters are appropriately quantized, the bound-state problems can be solved
solely by means of representation theory.Comment: 12 pages, 8 eepic figures; minor correction
Celebrating Faculty Scholarship: Bibliography - 2012
A bibliography of faculty publications submitted for inclusion in the fifth annual \u27Celebrating Faculty Scholarship\u27 event sponsored by Loyola University Libraries. The event, which took place on October 22, 2013 in the Richard J. Klarchek Information Commons on the university\u27s Lake Shore Campus, featured articles, books, creative works, and other materials authored by Loyola University Chicago faculty in 2012