ua nt - p h / 06 09 21 9 v 2 2 1 N ov 2 00 6 Eigenvalue problems for the complex PT - symmetric Potential V ( x ) = igx
نویسنده
چکیده
The spectrum of complex PT-symmetric potential, V (x) = igx, is known to be null. We enclose this potential in a hard-box: V (|x| ≥ 1) = ∞ and in a softbox: V (|x| ≥ 1) = 0. In the former case, we find real discrete spectrum and the exceptional points of the potential. The asymptotic eigenvalues behave as En ∼ n. The solvable purely imaginary PT-symmetric potentials vanishing asymptotically known so far do not have real discrete spectrum. Our solvable soft-box potential possesses two real negative discrete eigenvalues if |g| < (1.22330447). The soft-box potential turns out to be a scattering potential not possessing reflectionless states.
منابع مشابه
Se p 20 06 Eigenvalue problems with complex PT - symmetric Potential : V ( x ) = igx
The spectrum of complex PT-symmetric potential, V (x) = igx, is known to be null. We enclose this potential in a hard-box: V (|x| ≥ 1) = ∞ and in a softbox: V (|x| ≥ 1) = 0. In the former case, we find real discrete spectrum and the exceptional points of the potential. The asymptotic eigenvalues behave as En ∼ n. The solvable purely imaginary PT-symmetric potentials vanishing asymptotically kno...
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