The Inverse Eigenvalue Problem in Quantum Mechanics

D. I. Blokhint︠s︡ev

V. B. Gostev, В. С. Минеев, A. R. Frenkin

Eliot Bolduc

James Feigenbaum, Peter G. O. Freund

The algebra of observables of SOq(3)-symmetric quantum mechanics is extended to include the inverse 1/R of the radial coordinate and used to obtain eigenvalues and eigenfunctions of a q-deformed Coulomb Hamiltonian.

Asim Gangopadhyaya, Prasanta Kumar Panigrahi, U. Sukhatme

We analyse transition potentials, i.e. potentials exhibiting limiting inverse-square behaviour V(r) to r approximately 0 alpha r -2 in non-relativistic quantum mechanics using the techniques of supersymmetry. For the range - 1/4 <or= alpha < 3/4 , the eigenvalue problem becomes ill defined (since it is not possible to choose a unique eigenfunction based on square integrability and boundary conditions). It is shown that supersymmetric quantum mechanics (SUSYQM) provides a natural prescription for a unique determination of the spectrum. Interestingly, our SUSYQM-based approach picks out the same 'less singular' wavefunctions as the conventional approach and thus provides a simple justification for the usual practice in the literature. Two examples (the Poschl-Teller II potential and a two-anyon system on the plane) have been worked out for illustrative purposes.

Dean Lee