Non-hermitian quantum mechanics in non-commutative space |
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Authors: | Pulak Ranjan Giri and P Roy |
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Institution: | (1) Theory Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Calcutta, 700064, India;(2) Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, 700108, India |
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Abstract: | A recent investigation of the possibility of having a
-symmetric periodic potential in an optical lattice stimulated the urge to generalize non-hermitian quantum mechanics beyond
the case of commutative space. We thus study non-hermitian quantum systems in non-commutative space as well as a
-symmetric deformation of this space. Specifically, a
-symmetric harmonic oscillator together with an iC(x
1+x
2) interaction are discussed in this space, and solutions are obtained. We show that in the
deformed non-commutative space the Hamiltonian may or may not possess real eigenvalues, depending on the choice of the non-commutative
parameters. However, it is shown that in standard non-commutative space, the iC(x
1+x
2) interaction generates only real eigenvalues despite the fact that the Hamiltonian is not
-symmetric. A complex interacting anisotropic oscillator system also is discussed. |
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Keywords: | PACS" target="_blank">PACS 03 65 -w 03 65 Db 03 65 Ta |
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