Geodesic
Exactly solvable models in supersymmetric quantum mechanics and connection with spectrum-generating algebras
Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 3, pp. 362-374

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Analytic expressions for the eigenvalues and eigenfunctions of nonrelativistic shape-invariant Hamiltonians can be derived using the well-known method of supersymmetric quantum mechanics. Most of these Hamiltonians also possess spectrum-generating algebras and are hence solvable by an independent group theory method. We demonstrate the equivalence of the two solution methods by developing an algebraic framework for shape-invariant Hamiltonians with a general parameter change involving nonlinear extensions of Lie algebras. 
@article{TMF_1999_118_3_a5,
     author = {A. Gangopadhyaya and J. V. Mallow and C. Rasinariu and U. P. Sukhatme},
     title = {Exactly solvable models in supersymmetric quantum mechanics and connection with spectrum-generating algebras},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {362--374},
     publisher = {mathdoc},
     volume = {118},
     number = {3},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1999_118_3_a5/}
}
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A. Gangopadhyaya; J. V. Mallow; C. Rasinariu; U. P. Sukhatme. Exactly solvable models in supersymmetric quantum mechanics and connection with spectrum-generating algebras. Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 3, pp. 362-374. http://geodesic.mathdoc.fr/item/TMF_1999_118_3_a5/