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

O. D. Skoromnik, I. D. Feranchuk

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 se…