Perturbative renormalization in quantum mechanics

Lothar Schäfer

K.-I. Aoki, A. Horikoshi, M. Taniguchi +1 more

We analyze quantum mechanical systems using the non-perturbative renormalization group (NPRG). The NPRG method enables us to calculate quantum corrections systematically and is very effective for studying non-perturbative dynamics. We start with anharmonic oscillators and proceed to asymmetric double well potentials, supersymmetric quantum mechanics and many particle systems.

Pierre M. Pfeuty, Rémi Jullien, K. A. Penson

Francisco Marcelo Fernández

The accuracy of the renormalized perturbation series for anharmonic oscillators and other simple quantum-mechanical models increases with the quantum number when the adjustable parameter is determined by a simple variational criterion. In the semiclassical limit of quantum mechanics such an expansion converges towards the result of the Jeffreys–Wentzel–Kramers–Brillouin method to all orders. The hypervirial and Hellmann–Feynman theorems facilitate the derivation of the semiclassical series from Rayleigh–Schrödinger perturbation theory.

H. Jirari, H. Kröger, X.Q. Luo +2 more

Giovanni Amelino-camelia A

In bosonic and perturbative calculations for quantum mechanical anyon systems a regularization and renormalization procedure, analogous to those used in field theory, is necessary. I examine the reliability and the physical interpretation of the most commonly used bosonic end regularization procedures. I then use the regularization procedure with the most transparent physical intepretation to derive some bosnic end perturbation theory results on anyon spectra, including a three-anyon ground state energy.