Study of discontinuities in eigenvalue spectra of some model Hamiltonians
- 7 March 1989
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 22 (5) , 459-468
- https://doi.org/10.1088/0305-4470/22/5/012
Abstract
In this paper the authors study the eigenvalue spectra of two model s-wave Hamiltonians in three dimensions: H=p2/2-1/r+2 mu r+2 lambda 2r2 and H=p2/2+2 mu r+2 lambda 2r2. Using the method of Hill determinants they show that these eigenvalue spectra display discontinuities in the limit when both coupling constants mu and lambda vanish simultaneously. They use a simple variational calculation to argue that such discontinuities are characteristic of these Hamiltonians and are not an artefact of their numerical methods. In fact, such discontinuities are also to be seen in the case of a displaced harmonic oscillator in one dimension whose eigenvalue spectrum is exactly solvable.Keywords
This publication has 7 references indexed in Scilit:
- An example of a quantum catastropheJournal of Physics A: General Physics, 1988
- Polynomial perturbation of a hydrogen atomJournal of Physics A: General Physics, 1982
- Simple examples in singular perturbation theory: Eigenvalues that do not tend to the unperturbed values as the perturbation is switched offLettere al Nuovo Cimento (1971-1985), 1979
- A polynomial perturbation problemPhysics Letters A, 1978
- Eigenvalues of λx2m anharmonic oscillatorsJournal of Mathematical Physics, 1973
- The Hill Determinant: An Application to the Anharmonic OscillatorPhysical Review D, 1971
- Successive Approximations by the Rayleigh-Ritz Variation MethodPhysical Review B, 1933