Chun-Sheng Jia

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) = q2 tanh2 αx+i(q1/2) sech αx tanh αx + q0, q2 > 0. The discrete energy Eigenvalues of the latter complex potential are shown to be real when |q1| ≤ α2/2 + 2q2, while they are complex conjugate pairs if |q1| > α2/2 + 2q2. The PT symmetry is unbroken in the former case and spontaneously broken in the latter case.

Complexified Pöschl–Teller II potential model

Abstract With the help of complexifying a five-parameter exponential-type potential model, we obtain a general complex version of the Poschl–Teller II potential, V(x)=−V 1 q c q 0 sech q c 2 λx+V 2 q c q 0 cosech q c 2 λx , where qc=q0e2iαe, real V1>0, q0>0 and 0 π 2 . It has been shown that this complex potential is P-pseudo-Hermitian and PT-symmetric, where the parity operator P acts on the position operator as PxP −1 = ln q 0 λ −x . The discrete energy eigenvalues are shown to be real when V 2 ⩾− q 0 λ 2 4 while they are complex conjugate pairs if V 2 q 0 λ 2 4 .

A new η-pseudo-Hermitian complex potential with PT symmetry

Abstract Complexfying a five-parameter exponential-type potential with shape invariance, we obtain a new η-pseudo-Hermitian complex potential with PT symmetry, V(x)=(V1/q)tanhq2(αx)−iV2sechq(αx)·tanhq(αx), q>0 and q≠1. The discrete energy eigenvalues are shown to be real when |V 2 |⩽(1/ q )((α 2 q/4)+V 1 ) while they are complex conjugate pairs if |V 2 |>(1/ q )((α 2 q/4)+V 1 ) .

SYSTEMATIC STUDY ON EXACTLY SOLVABLE TRIGONOMETRIC POTENTIALS WITH PT SYMMETRY

We propose a unified treatment of generating exactly solvable trigonometric potentials with PT symmetry. Our symmetric approach reproduces a number of earlier results. We show that the energy spectra for the exactly solvable PT-symmetric trigonometric potentials can be obtained from a general energy spectrum formula.

NEW SOLVABLE PSEUDO-HERMITIAN POTENTIAL MODELS WITH REAL SPECTRA

We construct three new solvable pseudo-Hermitian potential models with real spectra starting from the five-parameter exponential-type potential model.