Fock Space Representations for Non-Hermitian Hamiltonians

Details Fock Space Representations for Non-Hermitian Hamiltonians Fock Space Representations for Non-Hermitian Hamiltonians

2004-12-14

arxiv.org/abs/hep-th/0412148v1

J.Phys. A38 (2005) 3611-3624

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX2e, 18 pages

Scientific paper

10.1088/0305-4470/38/16/010

The requirement of Hermiticity of a Quantum Mechanical Hamiltonian, for the description of physical processes with real eigenvalues which has been challenged notably by Carl Bender, is examined for the case of a Fock space Hamilitonian which is bilinear in two creation and destruction operators. An interpretation of this model as a Schr\"odinger operator leads to an identification of the Hermitian form of the Hamiltonian as the Landau model of a charged particle in a plane, interacting with a constant magnetic field at right angles to the plane. When the parameters of the Hamiltonian are suitably adjusted to make it non-Hermitian, the model represents two harmonic oscillators at right angles interacting with a constant magnetic field in the third direction, but with a pure imaginary coupling, and real energy eigenvalues. It is now ${\cal PT}$ symmetric. Multiparticle states are investigated.

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