Algebraic treatment of non-Hermitian quadratic Hamiltonians

Abstract

We generalize a recently proposed algebraic method in order to treat non-Hermitian Hamiltonians. The approach is applied to several quadratic Hamiltonians studied earlier by other authors. Instead of solving the Schr\"odinger equation we simply obtain the eigenvalues of a suitable matrix representation of the operator. We take into account the existence of unitary and antiunitary symmetries in the quantum-mechanical problem.