PT Symmetric Schrödinger Operators: Reality of the Perturbed Eigenvalues

Emanuela Caliceti
2010 Symmetry, Integrability and Geometry: Methods and Applications  
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 $-1<\epsilon<0$.
doi:10.3842/sigma.2010.009 fatcat:tc3lcui5gzbg3mxjowgzjiwaju