ANALYTIC AND ALGEBRAIC RELATIONS BETWEEN SOME CLASSICAL QUANTUM-MECHANICAL PROBLEMS

The combined use of the factorization theory, of the algebras arising from this theory and of the «no Inönu-Wigner contraction» suggests a general method for analysing the algebraic and analytic relations between some classical quantum-mechanical problems, that in principle can be applied to all the physical problems classified by Infeld and Hull. As an example we discuss explicitly the cases of the radial equations of the hydrogen atom, of the harmonic oscillator and of the constant potential. Because of the generality of the results, these problems are studied for arbitrary dimensions. We thus obtain a full understanding of the analytic and algebraic structures and relations of the three problems. The relation of our results with those reported in the literature is analysed. A generalization of the Bergmann-Frishmann relation is obtained. © 1968 Società Italiana di Fisica.