Analytic approximation for eigenvalues of a class of $\mathcal{P}\mathcal{T}$ symmetric Hamiltonians

Abstract

An analytical approximation for the eigenvalues of $\mathcal{P}\mathcal{T}$ symmetric Hamiltonian $\mathsf{H}=-d^2/d{x}^2-(\mathrm{i}x{)}^{\epsilon +2}$, $\epsilon >-1$ is developed via simple basis sets of harmonic-oscillator wave functions with variable frequencies and equilibrium positions. We demonstrate that our approximation provides high accuracy for any given energy level for all values of $\epsilon >-1$.

8 pages, 3 figures

References in corpus (10)

• Making Sense of Non-Hermitian Hamiltonians
• Loss-induced suppression and revival of lasing
• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• Visualization of Branch Points in PT-Symmetric Waveguides
• The ODE/IM Correspondence
• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• $PT$ Symmetric Real Dirac Fermions and Semimetals
• Bifurcation diagram and pattern formation in superconducting wires with electric currents
• Waveguides with Absorbing Boundaries: Nonlinearity Controlled by an Exceptional Point and Solitons
• Bound states emerging from below the continuum in a solvable PT-symmetric discrete Schroedinger equation