P T-symmetrically regularized Eckart, Pöschl-Teller and Hulthén potentials
Abstract
P T ( = parity times time-reversal) symmetry of complex Hamiltonians with real spectra is usually interpreted as a weaker mathematical substitute for Hermiticity. Perhaps an equally important role is played by the related strengthened analyticity assumptions. In a constructive illustration we complexify a few potentials solvable only in s-wave. Then we continue their domain from the semi-axis to the whole axis and obtain new exactly solvable models. Their energies turn out to be real as expected. The new one-dimensional spectra themselves differ quite significantly from their s-wave predecessors.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- June 2000
- DOI:
- 10.1088/0305-4470/33/24/311
- arXiv:
- arXiv:quant-ph/9912027
- Bibcode:
- 2000JPhA...33.4561Z
- Keywords:
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- Quantum Physics
- E-Print:
- Original 10-page letter ``PT-symmetrized exact solution of the singular Eckart oscillator" is extended to a full paper