| Abstract: | It is shown that the Jacobi algebraQJ(3) generates potentials that admit exact solution in relativistic and nonrelativistic quantum mechanics. Being a spectrum-generating dynamic 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 ofQJ(3).Donetsk State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 93, No. 1, pp. 3–16, October, 1992. |
