Adaptive Perturbation Theory I: Quantum Mechanics

Weinstein, Marvin

Stanford Linear Accelerator Center

关键词: Renormalization;    Coupling Constants;    Anharmonic Oscillators;    Tunneling Theory-Hep,Hepth, Phys;    Quantum Mechanics;   

DOI  :  10.2172/878047
RP-ID  :  SLAC-PUB-11260
RP-ID  :  AC02-76SF00515
RP-ID  :  878047

美国|英语

来源: UNT Digital Library

【 摘 要 】

Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that heretofore were not believed to be treatable by such methods. The novel feature of adaptive perturbation theory is that it decomposes a given Hamiltonian, H, into an unperturbed part and a perturbation in a way which extracts the leading non-perturbative behavior of the problem exactly. This paper introduces the method in the context of the pure anharmonic oscillator and then goes on to apply it to the case of tunneling between both symmetric and asymmetric minima. It concludes with an introduction to the extension of these methods to the discussion of a quantum field theory. A more complete discussion of this issue will be given in the second paper in this series, and it will show how to use the method of adaptive perturbation theory to non-perturbatively extract the structure of mass, wavefunction and coupling constant renormalization.