Exact eigenvalues of the Hamiltonian P2+A mod X modnu
- 1 April 1979
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 12 (4) , 451-457
- https://doi.org/10.1088/0305-4470/12/4/006
Abstract
The correspondence between operators on a Hilbert space and phase-space functions based upon symmetric ordering, introduced by Cahill and Glauber (1969) (Weyl correspondence) is used in the present paper to define (non-linear) unitary transformations for quantum systems with the help of canonical transformations, which are bijective, i.e. one-to-one onto. These unitary transformations can be used to determine exactly the energy eigenvalues of a large class of one-dimensional quantum systems. As an example the authors calculate the exact eigenvalues of the Hamiltonian H(X,P)=1/2m(P2+a12( nu +2)/ mod X mod nu ), a, nu >0.Keywords
This publication has 3 references indexed in Scilit:
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- Density Operators and Quasiprobability DistributionsPhysical Review B, 1969
- Ordered Expansions in Boson Amplitude OperatorsPhysical Review B, 1969