Analytic approximation for eigenvalues of a class of $\mathcal{P}\mathcal{T}$ symmetric Hamiltonians

Abstract

An analytical approximation for the eigenvalues of $\mathcal{P}\mathcal{T}$ symmetric Hamiltonian $\mathsf{H}=-d^2/d{x}^2-(\mathrm{i}x{)}^{\epsilon +2}$, $\epsilon >-1$ is developed via simple basis sets of harmonic-oscillator wave functions with variable frequencies and equilibrium positions. We demonstrate that our approximation provides high accuracy for any given energy level for all values of $\epsilon >-1$.

arXiv comment8 pages, 3 figures

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