Semiclassical approach to perturbation theory

Semiclassical perturbation approach to quantum reflection.

We consider the problem of quantum ‘‘reflection above the barrier,’’ introducing a distorted-wave Born approximation based on the primitive semiclassical Wentzel-Kramers-Brillouin wave function. The idea generalizes to the concept of an unperturbed Hamiltonian defined as the exact Hamiltonian plus small parts which ‘‘turn off’’ nonclassical processes such as barrier reflection and barrier tunne...

Semiclassical treatment of the logarithmic perturbation theory

The explicit semiclassical treatment of logarithmic perturbation theory for the nonrelativistic bound states problem is developed. Based upon ¯ h-expansions and suitable quantization conditions a new procedure for deriving perturbation expansions for the one-dimensional anharmonic oscillator is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same ...

Semiclassical perturbation theory for diffraction in heavy atom surface scattering.

The semiclassical perturbation theory formalism of Hubbard and Miller [J. Chem. Phys. 78, 1801 (1983)] for atom surface scattering is used to explore the possibility of observation of heavy atom diffractive scattering. In the limit of vanishing ℏ the semiclassical theory is shown to reduce to the classical perturbation theory. The quantum diffraction pattern is sensitive to the characteristics ...

A New Algebraic Approach to Perturbation Theory

An algebraic non-perturbative approach is proposed for the analytical treatment of Schrödinger equations with a potential that can be expressed in terms of an exactly solvable piece with an additional potential. Avoiding disadvantages of standard approaches, new handy recursion formulae with the same simple form both for ground and excited states have been obtained. As an illustration the proce...

Semiclassical Approach to Relativistic Nuclear Mean Field Theory