7 research outputs found
A family of complex potentials with real spectrum
We consider a two-parameter non hermitean quantum-mechanical hamiltonian that
is invariant under the combined effects of parity and time reversal
transformation. Numerical investigation shows that for some values of the
potential parameters the hamiltonian operator supports real eigenvalues and
localized eigenfunctions. In contrast with other PT symmetric models, which
require special integration paths in the complex plane, our model is integrable
along a line parallel to the real axis.Comment: Six figures and four table
Non-Hermitian matrix description of the PT symmetric anharmonic oscillators
Schroedinger equation H \psi=E \psi with PT - symmetric differential operator
H=H(x) = p^2 + a x^4 + i \beta x^3 +c x^2+i \delta x = H^*(-x) on
L_2(-\infty,\infty) is re-arranged as a linear algebraic diagonalization at
a>0. The proof of this non-variational construction is given. Our Taylor series
form of \psi complements and completes the recent terminating solutions as
obtained for certain couplings \delta at the less common negative a.Comment: 18 pages, latex, no figures, thoroughly revised (incl. title), J.
Phys. A: Math. Gen., to appea