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 $-1<\epsilon <0$.

References in corpus (8)

• Coupling of eigenvalues of complex matrices at diabolic and exceptional points
• Unfolding of eigenvalue surfaces near a diabolic point due to a complex perturbation
• Complexified Dynamical Systems
• Perturbation theory of PT-symmetric Hamiltonians
• Bounds on variation of spectral subspaces under J-self-adjoint perturbations
• $PT$ symmetric non-selfadjoint operators, diagonalizable and non-diagonalizable, with real discrete spectrum
• Small-$\epsilon$ behavior of the Non-Hermitian PT-Symmetric Hamiltonian $H=p^2+x^2(ix{)}^{\epsilon }$
• Real eigenvalues in non-Hermitian Hamilton quantum physics

Cited by in corpus (1)

• Anharmonic oscillators in the complex plane, $\mathcal{P}\mathcal{T}$-symmetry, and real eigenvalues