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arXiv · 1304.5692

Vector Models in PT Quantum Mechanics

Katherine Jones-Smith·Rudolph Kalveks
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Abstract

We present two examples of non-Hermitian Hamiltonians which consist of an unperturbed part plus a perturbation that behaves like a vector, in the framework of PT quantum mechanics. The first example is a generalization of the recent work by Bender and Kalveks, wherein the E2 algebra was examined; here we consider the E3 algebra representing a particle on a sphere, and identify the critical value of coupling constant which marks the transition from real to imaginary eigenvalues. Next we analyze a model with SO(3) symmetry, and in the process extend the application of the Wigner-Eckart theorem to a non-Hermitian setting.

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Katherine Jones-Smith, Rudolph Kalveks. 2013-04-21. Vector Models in PT Quantum Mechanics. https://doi.org/10.1007/s10773-013-1493-7

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