PT Symmetric Schrödinger Operators: Reality of the Perturbed Eigenvalues

Abstract

We prove the reality of the perturbed eigenvalues of some PT symmetric Hamiltonians of physical interest by means of stability methods. In particular we study 2-dimensional generalized harmonic oscillators with polynomial perturbation and the one-dimensional $x^2(ix{)}^{\epsilon }$ for $-1<\epsilon <0$.

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Cited by in corpus (2)

• Discrete spectrum of thin PT-symmetric waveguide
• Anharmonic oscillators in the complex plane, $\mathcal{P}\mathcal{T}$-symmetry, and real eigenvalues