Approximations to path integrals and spectra of quantum systems

Simple item page
dc.creatorBlinnikov, S. I.
dc.creatorNikitin, N. V.
dc.date2003-09-14
dc.date.accessioned2026-07-07T05:50:00Z
dc.date.available2026-07-07T05:50:00Z
dc.descriptionAn expression for the Green function G(E;x_1,x_2) of the Schroedinger equation is obtained through the approximations of the path integral by n-fold multiple integrals. The approximations to Re{G(E;x,x)} on the real E-axis have peaks near the values of the energy levels E_{j}. The analytic and numerical examples for one-dimensional and multi-dimensional harmonic and anharmonic oscillators, and Poeschl-Teller potential wells, show that median values of these peaks for approximate G(E;0,0) corresponds with accuracy of order 10% to the exact values of even levels already in the lowest orders of approximation n=1 and n=2, i.e. when the path integral is replaced by a line or double integral. The weights of the peaks approximate the values of the squared modulus of the wave functions at x=0 with the same accuracy.
dc.description16 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/physics/0309060
dc.identifierhttp://arxiv.org/abs/physics/0309060
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/85589
dc.subjectComputational Physics
dc.subjectHigh Energy Physics - Theory
dc.subjectAtomic Physics
dc.subjectQuantum Physics
dc.titleApproximations to path integrals and spectra of quantum systems
dc.typetext

Files

Collections

arXiv