FAST TRACK COMMUNICATION: Conjecture on the analyticity of {\cal PT} -symmetric potentials and the reality of their spectra
Abstract
The spectrum of the Hermitian Hamiltonian H = p2 + V(x) is real and discrete if the potential V(x) → ∞ as x → ±∞. However, if V(x) is complex and \cal{PT} -symmetric, it is conjectured that, except in rare special cases, V(x) must be analytic in order to have a real spectrum. This conjecture is demonstrated by using the potential V(x) = (ix)a|x|b, where a, b are real.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- October 2008
- DOI:
- 10.1088/1751-8113/41/39/392005
- arXiv:
- arXiv:0807.0424
- Bibcode:
- 2008JPhA...41M2005B
- Keywords:
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- Mathematical Physics;
- High Energy Physics - Theory
- E-Print:
- 8 Pages, 2 figures