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Solution of an analogous Schrödinger equation for $\mathcal{PT}$-symmetric sextic potential in two dimensions
Fakir Chand S C Mishra Ram Mehar Singh
Volume 73 Issue 2 August 2009 pp 349-361
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Keywords
Schrödinger equation ;complex Hamiltonian ;$\mathcal{PT}$ symmetry ;eigenvalues and eigenfunctions. -
Abstract
We investigate the quasi-exact solutions of an analogous Schrödinger wave equation for two-dimensional non-Hermitian complex Hamiltonian systems within the framework of an extended complex phase space characterized by $x = x_{1} + ip_{3}$, $y = x_{2} + ip_{4}$, $p_{x} = p_{1} + ix_{3}$, $p_{y} = p_{2} + ix_{4}$. Explicit expressions for the energy eigenvalues and eigenfunctions for ground and first excited states of a two-dimensional $\mathcal{PT}$-symmetric sextic potential and some of its variants are obtained. The eigenvalue spectra are found to be real within some parametric domains.
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Author Affiliations
Fakir Chand1 S C Mishra1 Ram Mehar Singh2
- Department of Physics, Kurukshetra University, Kurukshetra 136 119, India
- Department of Physics, Ch. Devi Lal University, Sirsa 125 055, India
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Dates
- Published
- August 2009
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Pramana – Journal of Physics
Volume 96, 2022
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