Continuum states in generalized Swanson models

Details Continuum states in generalized Swanson models Continuum states in generalized Swanson models

2009-01-07

arxiv.org/abs/0901.0804v1

J. Phys. A: Math. Theor. vol. 42 (2009) 052002 (9pp)

Physics

Quantum Physics

12 pages, 2 figures

Scientific paper

A one-to-one correspondence is known to exist between the spectra of the discrete states of the non Hermitian Swanson-type Hamiltonian $ H = {\cal{A}}^{\dagger} {\cal{A}} + \alpha {\cal{A}} ^2 + \beta {\cal{A}}^{\dagger 2} $, ($\alpha \neq \beta $), and an equivalent Hermitian Schr\"{o}dinger Hamiltonian $h$, the two Hamiltonians being related through a similarity transformation. In this work we consider the continuum states of $h$, and examine the nature of the corresponding states of $H$.

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