Quasi-exact minus-quartic oscillators in strong-core regime

Abstract

PT-symmetric potentials $V(x)=-x^4+jB{x}^3+C{x}^2+jDx+jF/x+G/x^2$ are quasi-exactly solvable, i.e., a specific choice of a small $G=G^{(QES)}=integer/4$ is known to lead to wave functions ${\psi }^{(QES)}(x)$ in closed form at certain charges $F=F^{(QES)}$ and energies $E=E^{(QES)}$. The existence of an alternative, simpler and non-numerical version of such a construction is announced here in the new dynamical regime of very large $G^{(QES)}\to \infty$.

References in corpus (3)

• An Equivalent Hermitian Hamiltonian for the non-Hermitian -x^4 Potential
• Third order spectral branch points in Krein space related setups: PT-symmetric matrix toy model, MHD alpha^2-dynamo, and extended Squire equation
• Perturbation method for non-square Hamiltonians and its application to polynomial oscillators

Cited by in corpus (2)

• PT-symmetric quartic anharmonic oscillator and position-dependent mass in a perturbative approach
• PT-Symmetric, Quasi-Exactly Solvable matrix Hamiltonians