Abstract:
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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