Quantum Particle in a PT-symmetric Well

ABSTRACT: In this thesis, we study the role of boundary conditions via -symmetric quantum mechanics. Where denotes parity operator and denotes time reversal operator. We present the boundary conditions so that the -symmetry remains unbroken. We give exact solvable solutions for a free particle in a box. In the first approach, we consider one dimensional Schrödinger Hamiltonian for a free particle in an infinite well. The energy equation is obtained and the results for the Eigenfunctions of the -symmetry are observed completely different form the usual textbooks ones. The second approach is the solution of the Klein Gordon equation in dimensions for the free particle in an infinite well. For both cases, the -symmetric eigenfunctions are normalized and plotted. The asymptotic behavior of the eigenfunction is provided. We consider a variational principle for -symmetric quantum system and examine an invertible linear operator ̂ for a weak-pseudo-hermicity generators for non-Hermitian Hamiltonian. 11  Keywords: Hamiltonian, -symmetric Quantum Mechanics, Variational Principle, Eigenvalues and Eigenfunctions. …………………………………………………………………………………………………………………………