Electronic Resource
College Park, Md.
:
American Institute of Physics (AIP)
Journal of Mathematical Physics
31 (1990), S. 2579-2585
ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
The possibility of expressing the solution to a φ2P quantum field theory as a series in powers of 1/P is proposed. Such a series would be nonperturbative in its dependence on the fundamental parameters of the theory such as the mass and the coupling constant. The first term in such a series describes a field in an infinite-dimensional square-well potential. In this paper, the quantum-mechanical Hamiltonian H=p2+q2P is studied as a model calculation and the expansion of the energy levels as series in powers of 1/P is examined. The method of matched asymptotic expansions to determine the first five terms in the series for all energy levels is used. The results are compared with extensive numerical calculations of the ground-state energy and it is found that the series is extremely accurate: When P=2, the five-term series has a relative error of 6%, when P=10 the relative error is 0.009%, and when P=200 the relative error is 3.4×10−9%.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.529006
Permalink
Library |
Location |
Call Number |
Volume/Issue/Year |
Availability |