Semiclassical analysis of a complex quartic Hamiltonian
Abstract
It is necessary to calculate the C operator for the nonHermitian PTsymmetric Hamiltonian H=(1)/(2)p^{2}+(1)/(2)μ^{2}x^{2}λx^{4} in order to demonstrate that H defines a consistent unitary theory of quantum mechanics. However, the C operator cannot be obtained by using perturbative methods. Including a small imaginary cubic term gives the Hamiltonian H=(1)/(2)p^{2}+(1)/(2)μ^{2}x^{2}+igx^{3}λx^{4}, whose C operator can be obtained perturbatively. In the semiclassical limit all terms in the perturbation series can be calculated in closed form and the perturbation series can be summed exactly. The result is a closedform expression for C having a nontrivial dependence on the dynamical variables x and p and on the parameter λ.
 Publication:

Physical Review D
 Pub Date:
 January 2006
 DOI:
 10.1103/PhysRevD.73.025002
 arXiv:
 arXiv:quantph/0509034
 Bibcode:
 2006PhRvD..73b5002B
 Keywords:

 11.30.Er;
 02.30.Mv;
 12.38.Bx;
 Charge conjugation parity time reversal and other discrete symmetries;
 Approximations and expansions;
 Perturbative calculations;
 Quantum Physics;
 High Energy Physics  Theory
 EPrint:
 4 pages