Symmetry transforms of spherically symmetric Hamiltonians for different values of pertinent space dimensions

Symmetry transforms in $N_2$ space dimensions of $N_1$-dimensional spherically symmetric Schrödinger Hamiltonians have been treated for $N_2$≠$N_1$. Accordingly, the quantum number of the angular momentum and the number of space dimensions become subject to related mappings. One proceeds using suitable transformations of the radial coordinate and of the radial state function so as to exhibit the form invariance of the Laplace operator. The symmetries established in this way concern potentials which can be represented by power-series expansions. Such symmetry transforms are generated by rational values of underlying power exponents. Symmetry properties of 1/N energy estimates are also discussed.