|
Booksee.org
Anharmonic oscillatorBender, Wu.We consider the anharmonic oscillator defined by the differential equation and the boundary condition limit of Φ(x) as x→+∞=0. This model is interesting because the perturbation series for the ground-state energy diverges. To investigate the reason for this divergence, we analytically continue the energy levels of the Hamiltonian H into the complex λ plane. Using WKB techniques, we find that the energy levels as a function of λ, or more generally of λ^α, have an infinite number of branch points with a limit point at λ=0. Thus, the origin is not an isolated singularity. Level crossing occurs at each branch point. If we choose α=1 / 3, the resolvent (z-H)^(-1) has no branch cut. However, for all z it has an infinite sequence of poles which have a limit point at the origin. The anharmonic oscillator is of particular interest to field theoreticians because it is a model of λϕ^4 field theory in one-dimensional space-time. The unusual and unexpected properties exhibited by this model may give some indication of the analytic structure of a more realistic field theory.
Ссылка удалена правообладателем ---- The book removed at the request of the copyright holder.
Популярные книги за неделю:
#3
Самодельные детали для сельского радиоприемникаАвторы: З.Б.Гинзбург, Ф.И.Тарасов.Категория: радиоэлектроника
1.40 Mb
#10
Вероятность и статистика. 10-11 классыБродский И.Л., Мешавкина О.С.Категория: M_Mathematics, MSch_School-level
1.24 Mb
Только что пользователи скачали эти книги:
#4
Multivariate Bayesian Statistics: Models for Source Separation and Signal UnmixingDaniel B. Rowe#5
Вальсируя с Медведями: управление рисками в проектах по разработке программного обеспеченияТом ДеМарко, Тимоти Листер
4.19 Mb
#9
DeWitt B.S. Dynamical Theory in Curved Spaces. I. A Review of the Classical and Quantum Action Principles (Rev.Mod.Phys.29,p377,1957)(600dpi)(T)(21s).djvu
589 Kb
|
|