Geodesic
Jacobi algebra and potentials generated by it
Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 1, pp. 3-16

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It is shown that the Jacobi algebra $QJ(3)$ generates potentials that admit exact solution in relativistic and nonrelativistic quantum mechanics. Being a spectrum-generatingdynamic symmetry algebra and possessing the ladder property, $QJ(3)$ makes it possible to find the wave functions in the coordinate representation. The exactly solvable potentials specified in explicit form are regarded as a special case of a larger class of exactly solvable potentials specified implicitly. The connection between classical and quantum problems possessing exact solutions is obtained by means of $QJ(3)$. 
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     author = {I. M. Lutsenko},
     title = {Jacobi algebra and potentials generated by it},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {3--16},
     publisher = {mathdoc},
     volume = {93},
     number = {1},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1992_93_1_a0/}
}
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I. M. Lutsenko. Jacobi algebra and potentials generated by it. Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 1, pp. 3-16. http://geodesic.mathdoc.fr/item/TMF_1992_93_1_a0/