Superconvergent Perturbation Method in Quantum Mechanics

Superconvergent perturbation method in quantum mechanics.

An analogue of Kolmogorov’s superconvergent perturbation theory in classical mechanics is constructed for self adjoint operators. It is different from the usual Rayleigh–Schrödinger perturbation theory and yields expansions for eigenvalues and eigenvectors in terms of functions of the perturbation parameter. PACS Code: 03.65.-w, 31.15+q, 02.30.Mv, 02.90.+p

Strong Coupling Perturbation Theory in Quantum Mechanics

We present a full introduction to the recent devised perturbation theory for strong coupling in quantum mechanics. In order to put the theory in a proper historical perspective, the approach devised in quantum field theory is rapidly presented, showing how it implies a kind of duality in perturbation theory, from the start. The approach of renormalization group in perturbation theory is then pr...

Time-dependent Perturbation Theory in Quantum Mechanics

After revealing difficulties of the standard time-dependent perturbation theory in quantum mechanics mainly from the viewpoint of practical calculation, we propose a new quasi-canonical perturbation theory. In the new theory, the dynamics of physical observables, instead of that of coefficients of wave-function expansion, is formulated so that the gauge-invariance and correspondence principles ...

The Stochastic Perturbation Method for Computational Mechanics

Numerical Constructions of Perturbation Series in Quantum Mechanics

Our several recent improvements of the current textbook (so called Rayleigh-Schrödinger) perturbative representation of bound states are reviewed. They were all inspired by an adaptive re-split H(λ) = H + λH of the Hamiltonian. Their feasibility is facilitated by the use of nonstandard bases and by the flexibility of normalization of the wave functions ψ(λ).