Abstract
We study the path integral solution of a system of particle moving in certain class of PT symmetric non-Hermitian and non-central potential. The Hamiltonian of the system is converted to a separable Hamiltonian of Liouville type in parabolic coordinates and is further mapped into a Hamiltonian corresponding to two 2-dimensional simple harmonic oscillators (SHOs). Thus the explicit Green’s functions for a general non-central PT symmetric non hermitian potential are calculated in terms of that of 2d SHOs. The entire spectrum for this three dimensional system is shown to be always real leading to the fact that the system remains in unbroken PT phase all the time.
Keywords
- Annihilation Operator
- Canonical Transformation
- Path Integral Formulation
- Liouville Type
- Simple Harmonic Oscillator
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Acknowledgments
BPM acknowledge the financial support from the Department of Science and Technology (DST), Govt. of India under SERC project sanction grant No. SR/S2/HEP-0009/2012.
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Mourya, B.K., Mandal, B.P. (2016). Green’s Function of a General PT-Symmetric Non-Hermitian Non-central Potential. In: Bagarello, F., Passante, R., Trapani, C. (eds) Non-Hermitian Hamiltonians in Quantum Physics. Springer Proceedings in Physics, vol 184. Springer, Cham. https://doi.org/10.1007/978-3-319-31356-6_21
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DOI: https://doi.org/10.1007/978-3-319-31356-6_21
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