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arXiv · 1507.03644

Three PT-symmetric Hamiltonians with completely different spectra

Francisco M. Fernández·Javier Garcia
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Abstract

We discuss three Hamiltonians, each with a central-field part $H_{0}$ and a PT-symmetric perturbation $igz$. When $H_{0}$ is the isotropic Harmonic oscillator the spectrum is real for all $g$ because $H$ is isospectral to $H_{0}+g^{2}/2$. When $H_{0}$ is the Hydrogen atom then infinitely many eigenvalues are complex for all $g$. If the potential in $H_{0}$ is linear in the radial variable $r$ then the spectrum of $H$ exhibits real eigenvalues for $0<g<g_{c}$ and a PT phase transition at $g_c$.

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Francisco M. Fernández, Javier Garcia. 2015-07-13. Three PT-symmetric Hamiltonians with completely different spectra. https://arxiv.org/abs/1507.03644

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