Level crossings in complex two-dimensional potentials |
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Authors: | Qing-Hai Wang |
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Institution: | (2) Dipartimento di Fisica, Universit? di Pisa, Pisa, Italy;(3) Istituto Nazionale di Fisica Nucleare, Sezione di Pisa, Pisa, Italy; |
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Abstract: | Two-dimensional $
\mathcal{P}\mathcal{T}
$
\mathcal{P}\mathcal{T}
-symmetric quantum-mechanical systems with the complex cubic potential V
12 = x
2 + y
2 + igxy
2 and the complex Hénon-Heiles potential V
HH = x
2 +y
2 +ig(xy
2 −x
3/3) are investigated. Using numerical and perturbative methods, energy spectra are obtained to high levels. Although both
potentials respect the $
\mathcal{P}\mathcal{T}
$
\mathcal{P}\mathcal{T}
symmetry, the complex energy eigenvalues appear when level crossing happens between same parity eigenstates. |
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Keywords: | |
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