0000000000409987

AUTHOR

Francisco M. Fernández

A family of complex potentials with real spectrum

We consider a two-parameter non-Hermitian quantum mechanical Hamiltonian operator that is invariant under the combined effects of parity and time reversal transformations. Numerical investigation shows that for some values of the potential parameters the Hamiltonian operator supports real eigenvalues and localized eigenfunctions. In contrast with other parity times time reversal symmetric models which require special integration paths in the complex plane, our model is integrable along a line parallel to the real axis.

research product

Riccati-Padé quantization and oscillatorsV(r)=grα

We develop an alternative construction of bound states based on matching the Riccati threshold and asymptotic expansions via their two-point Pad\'e interpolation. As a form of quantization it gives highly accurate eigenvalues and eigenfunctions.

research product

QUANTIZATION CONDITION FOR HIGHLY EXCITED STATES

We develop a quantization condition for the excited states of simple quantum-mechanical models. The approach combines perturbation theory for the oscillatory part of the eigenfunction with a rational approximation to the logarithmic derivative of the nodeless part of it. We choose one-dimensional anharmonic oscillators as illustrative examples.

research product

Computer algebra and large scale perturbation theory

This work presents a brief resume of our applications of computer algebra to the study of large-scale perturbation theory in quantum mechanical systems, both in the small and in the strong coupling regimes.

research product

Strong-coupling expansions for the -symmetric oscillators

We study the traditional problem of convergence of perturbation expansions when the hermiticity of the Hamiltonian is relaxed to a weaker symmetry. An elementary and quite exceptional cubic anharmonic oscillator is chosen as an illustrative example of such models. We describe its perturbative features paying particular attention to the strong-coupling regime. Efficient numerical perturbation theory proves suitable for such a purpose.

research product