Mathematical Aspects of Quantum Systems with a Pseudo-Hermitian Hamiltonian
A non-self-adjoint bosonic Hamiltonian H possessing real eigenvalues is investigated. It is shown that the operator can be diagonalized by making use of pseudo-bosonic operators. The biorthogonal sets of eigenvectors for the Hamiltonian and its adjoint are explicitly constructed. The positive definite operator which connects both sets of eigenvectors is also given. The dynamics of the model is briefly analyzed.
KeywordsPseudo-Hermitian Hamiltonians Non-Hermitian Hamiltonians with real eigenvalues Pseudo-bosons
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