Non-Hermitian PT-symmetric Sturm-Liouville operators and to them similar self-adjoint Hamiltonians
Jakub Zelezny,
(Nuclear Physics Institute ASCR, Rez, Czech Republic)
Martes 5 de abril 2011
In PT-symmetric quantum mechanics one interprets non-self adjoint
operators as self-adjoint ones in a different Hilbert space
with scalar product modifed using the so-called metric operator.
We present a simple PT-symmetric model based on the one-dimensional
Laplacian with non-Hermitian Robin-type boundary conditions
and derive a closed integral formula for its general metric operator.
We then use this formula to find the special case of the metric operator
related to the so called C operator in the Krein space reformulation
of the problem. This is a joint work with David Krejcirik and Petr Siegl.