<atl>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 <f>V(x)=q2tanh2αx+i(q1/2)sechαxtanhαx+q0</f>, <f>q2>0</f>. The discrete energy eigenvalues of the latter complex potential are shown to be real when <f>&z.sfnc;q1&z.sfnc;&les;α2/2+2q2</f>, while they are complex conjugate pairs if <f>&z.sfnc;q1&z.sfnc;>α2/2+2q2</f>. The PT symmetry is unbroken in the former case and spontaneously broken in the latter case. [Copyright &y& Elsevier]