Calculation of the hidden symmetry operator in P Tsymmetric quantum mechanics
Abstract
In a recent paper it was shown that if a Hamiltonian H has an unbroken Script PScript T symmetry, then it also possesses a hidden symmetry represented by the linear operator Script C. The operator Script C commutes with both H and Script PScript T. The inner product with respect to Script CScript PScript T is associated with a positive norm and the quantum theory built on the associated Hilbert space is unitary. In this paper it is shown how to construct the operator Script C for the nonHermitian Script PScript Tsymmetric Hamiltonian H = 1/2p^{2} + 1/2x^{2} + iepsilonx^{3} using perturbative techniques. It is also shown how to construct the operator Script C for H = 1/2p^{2} + 1/2x^{2}  epsilonx^{4} using nonperturbative methods.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 February 2003
 DOI:
 10.1088/03054470/36/7/312
 arXiv:
 arXiv:quantph/0211166
 Bibcode:
 2003JPhA...36.1973B
 Keywords:

 Quantum Physics
 EPrint:
 doi:10.1088/03054470/36/7/312