  In a recent paper it was shown that if a Hamiltonian H has an unbroken PT
symmetry, then it also possesses a hidden symmetry represented by the linear
operator C. The operator C commutes with both H and PT. The inner product with
respect to CPT 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 C for the non-Hermitian PT-symmetric Hamiltonian
$H={1\over2}p^2+{1\over2}x^2 +i\epsilon x^3$ using perturbative techniques. It
is also shown how to construct the operator C for
$H={1\over2}p^2+{1\over2}x^2-\epsilon x^4$ using nonperturbative methods.

Quantum Physics