Affiliation:
1. Faculty of Education, Ibaraki University, Bunkyo 2-1-1, Mito Japan
2. Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Copenhagen Ø, Denmark
Abstract
Abstract
In a special representation of complex action theory that we call “future-included,” we study a harmonic oscillator model defined with a non-normal Hamiltonian $\hat{H}$, in which a mass $m$ and an angular frequency $\omega$ are taken to be complex numbers. In order for the model to be sensible some restrictions on $m$ and $\omega$ are required. We draw a phase diagram in the plane of the arguments of $m$ and $\omega$, according to which the model is classified into several types. In addition, we formulate two pairs of annihilation and creation operators, two series of eigenstates of the Hamiltonians $\hat{H}$ and $\hat{H}^\dagger$, and coherent states. They are normalized in a modified inner product $I_Q$, with respect to which the Hamiltonian $\hat{H}$ becomes normal. Furthermore, applying to the model the maximization principle that we previously proposed, we obtain an effective theory described by a Hamiltonian that is $Q$-Hermitian, i.e. Hermitian with respect to the modified inner product $I_Q$. The generic solution to the model is found to be the “ground” state. Finally we discuss what the solution implies.
Publisher
Oxford University Press (OUP)
Subject
General Physics and Astronomy
Cited by
2 articles.
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1. Automatic hermiticity for mixed states;Progress of Theoretical and Experimental Physics;2023-02-16
2. Reality from maximizing overlap in the periodic complex action theory;Progress of Theoretical and Experimental Physics;2022-07-23