Eigenspectra of a complex coupled harmonic potential in three dimensions
| Autor: | S. B. Bhardwaj, S. C. Mishra, Ram Mehar Singh |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Mathematical analysis
Harmonic potential Mathematics::Spectral Theory Eigenfunction Schrödinger equation Computational Mathematics symbols.namesake Computational Theory and Mathematics Modeling and Simulation Phase space symbols Hamiltonian (quantum mechanics) Eigenvalues and eigenvectors Mathematics Ansatz |
| Zdroj: | Computers & Mathematics with Applications. 68:2068-2079 |
| ISSN: | 0898-1221 |
| DOI: | 10.1016/j.camwa.2014.09.006 |
| Popis: | Within the framework of extended complex phase space approach characterized by position and momentum coordinates, we investigate the quasi-exact solutions of the Schrodinger equation for a coupled harmonic potential and its variants in three dimensions. For this purpose ansatz method is employed and nature of the eigenvalues and eigenfunctions is determined by the analyticity property of the eigenfunctions alone. The energy eigenvalue is real for the real coupling parameters and becomes complex if the coupling parameters are complex. However, in case of complex coupling parameters, the imaginary component of energy eigenvalue reduces to zero if the P T -symmetric condition is satisfied. Thus a non-hermitian Hamiltonian possesses real eigenvalue if it is P T -symmetric. |
| Databáze: | OpenAIRE |
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