PT Symmetric Schr\"odinger Operators: Reality of the Perturbed Eigenvalues
classification
🧮 math-ph
math.MPquant-ph
keywords
eigenvaluesepsilonperturbedrealitysymmetricdimensionalgeneralizedhamiltonians
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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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