The relativistic rotated harmonic oscillator

Abstract

We introduce a relativistic version of the non-self-adjoint operator obtained by a dilation analytic transformation of the quantum harmonic oscillator. While the spectrum is real and discrete, we show that the eigenfunctions do not form a basis and that the pseudospectra are highly non-trivial.

3 figures

References in corpus (14)

• Pseudospectra in non-Hermitian quantum mechanics
• Relativistic quantum mechanics of a Dirac oscillator
• Examples of Pseudo-bosons in quantum mechanics
• Non-self-adjoint harmonic oscillator, compact semigroups and pseudospectra
• Eigenvalue estimates for non-selfadjoint Dirac operators on the real line
• Spectral projections and resolvent bounds for partially elliptic quadratic differential operators
• Eigenvalues of one-dimensional non-self-adjoint Dirac operators and applications
• Location of eigenvalues of non-self-adjoint discrete Dirac operators
• Location of eigenvalues of three-dimensional non-self-adjoint Dirac operators
• Eigenvalue bounds for non-selfadjoint Dirac operators
• Resolvent estimates for one-dimensional Schrödinger operators with complex potentials
• Pseudomodes for non-self-adjoint Dirac operators
• Localization of eigenvalues for non-self-adjoint Dirac and Klein-Gordon operators
• Keller-type bounds for Dirac operators perturbed by rigid potentials