PT symmetry and shape invariance for a potential well with a barrier

We construct an exponential-type PT-symmetric potential, which includes the PT-symmetric versions of the Rosen–Morse well and Scarf potential and the complex PT-invariant potential well V( x)= q 2tanh 2 αx+ i( q 1/2)sech αxtanh αx+ q 0, q 2>0. The discrete energy eigenvalues of the latter complex...

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Bibliographic Details
Published in:Physics letters. A 2002-02, Vol.294 (3), p.185-189
Main Authors: Jia, Chun-Sheng, Zeng, Xiang-Lin, Sun, Liang-Tian
Format: Article
Language:English
Subjects:
Energy eigenvalue
PT symmetry
Shape invariance
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Summary:We construct an exponential-type PT-symmetric potential, which includes the PT-symmetric versions of the Rosen–Morse well and Scarf potential and the complex PT-invariant potential well V( x)= q 2tanh 2 αx+ i( q 1/2)sech αxtanh αx+ q 0, q 2>0. The discrete energy eigenvalues of the latter complex potential are shown to be real when | q 1|⩽ α 2/2+2 q 2, while they are complex conjugate pairs if | q 1|> α 2/2+2 q 2. The PT symmetry is unbroken in the former case and spontaneously broken in the latter case.
ISSN:0375-9601
1873-2429
DOI:10.1016/S0375-9601(01)00840-4