CHINESE JOURNAL OF PHYSICS VOL. 39, NO. 2 APRIL 2001

Exact Solutions of the Schröedinger Equation:
Connection between Supersymmetric Quantum Mechanics
and Spectrum Generating Algebras

Asim Gangopadhyaya^1,a, Jeffry V. Mallow^1,b, Constantin Rasinariu^2,c and Uday P. Sukhatme^{3,d 1}Department of Physics, Loyola University Chicago, Chicago, Illinois 60605, USA

²Department of Science and Mathematics, Columbia College Chicago, Chicago, Illinois 60605, USA

³Department of Physics, University of Illinois at Chicago, Chicago, Illinois 60605, USA
(Received September 15, 2000)

Using supersymmetric quantum mechanics, one can obtain analytic expressions for the eigenvalues and eigenfunctions for all nonrelativistic shape invariant Hamiltonians. These Hamiltonians also possess spectrum generating algebras and are hence solvable by an independent, group theoretical method. In this paper, we demonstrate the equivalence of the two methods of solution, and review related progress in this field.

PACS. 03.65.-w - Quantum mechanics.
PACS. 03.65.Fd - Algebraic methods.

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