Matches in SemOpenAlex for { <https://semopenalex.org/work/W2000920261> ?p ?o ?g. }
Showing items 1 to 58 of
58
with 100 items per page.
- W2000920261 endingPage "1235" @default.
- W2000920261 startingPage "1219" @default.
- W2000920261 abstract "A concept of approximate dynamical symmetry is formulated by means of which we are able to produce approximate solutions to scattering and bound-state problems in a purely group-theoretic manner for essentially any isotropic potential and to any desired degree of accuracy. This concept forms a natural generalization to arbitrary potentials of the familiar Runge-Lenz symmetry of the Coulomb problem and the ${mathrm{SU}}_{3}$ symmetry of the harmonic oscillator. The method consists in transforming the dynamical Lie algebra, i.e., the smallest algebra generated by the Hamiltonian and a complete set of dynamical variables, which is usually infinite and simple, into a finite, simple Lie algebra as follows. We first transform the dynamical algebra into another infinite Lie algebra, but one which contains a large ideal, by a process similar to Inonu-Wigner contraction, the angular momentum acting as the contraction parameter. The factor algebra modulo this ideal turns out to be a finite, simple Lie algebra which still contains some of the dynamical information. The above two-stage process will be called truncation. We are able to develop a sequence of such truncations leading to successively higher dimensional simple Lie algebras whereby we obtain successively better approximations to energy levels and phase shifts. The solutions obtained involve all powers of the coupling constant, and the $N$th-order approximation is at least as good as the $N$th-order W.K.B. approximation and probably better. The special role of the angular momentum in the contraction process enables us to relate these group-theoretic methods to the Regge formalism in a natural way. In fact we are able, thereby, to produce exact solutions to dispersion relations for Regge trajectories obtained by including an arbitrarily large but finite set of trajectories in the unitarity relation. As an illustration of the methods developed we include a calculation to the first nontrivial order of energy levels of an anharmonic oscillator and the well-depth parameter and phase shifts for a Yukawa potential." @default.
- W2000920261 created "2016-06-24" @default.
- W2000920261 creator A5001553213 @default.
- W2000920261 date "1966-02-25" @default.
- W2000920261 modified "2023-09-24" @default.
- W2000920261 title "Solution of Scattering and Bound-State Problems by Construction of Approximate Dynamical Symmetries" @default.
- W2000920261 cites W1978291631 @default.
- W2000920261 cites W2015683036 @default.
- W2000920261 cites W2029500107 @default.
- W2000920261 cites W2159498395 @default.
- W2000920261 cites W3043212164 @default.
- W2000920261 cites W4230880638 @default.
- W2000920261 doi "https://doi.org/10.1103/physrev.142.1219" @default.
- W2000920261 hasPublicationYear "1966" @default.
- W2000920261 type Work @default.
- W2000920261 sameAs 2000920261 @default.
- W2000920261 citedByCount "15" @default.
- W2000920261 crossrefType "journal-article" @default.
- W2000920261 hasAuthorship W2000920261A5001553213 @default.
- W2000920261 hasConcept C121332964 @default.
- W2000920261 hasConcept C202444582 @default.
- W2000920261 hasConcept C2524010 @default.
- W2000920261 hasConcept C33923547 @default.
- W2000920261 hasConcept C37914503 @default.
- W2000920261 hasConcept C51568863 @default.
- W2000920261 hasConcept C62520636 @default.
- W2000920261 hasConcept C73648015 @default.
- W2000920261 hasConcept C96469262 @default.
- W2000920261 hasConceptScore W2000920261C121332964 @default.
- W2000920261 hasConceptScore W2000920261C202444582 @default.
- W2000920261 hasConceptScore W2000920261C2524010 @default.
- W2000920261 hasConceptScore W2000920261C33923547 @default.
- W2000920261 hasConceptScore W2000920261C37914503 @default.
- W2000920261 hasConceptScore W2000920261C51568863 @default.
- W2000920261 hasConceptScore W2000920261C62520636 @default.
- W2000920261 hasConceptScore W2000920261C73648015 @default.
- W2000920261 hasConceptScore W2000920261C96469262 @default.
- W2000920261 hasIssue "4" @default.
- W2000920261 hasLocation W20009202611 @default.
- W2000920261 hasOpenAccess W2000920261 @default.
- W2000920261 hasPrimaryLocation W20009202611 @default.
- W2000920261 hasRelatedWork W1989908416 @default.
- W2000920261 hasRelatedWork W2001138128 @default.
- W2000920261 hasRelatedWork W2086467967 @default.
- W2000920261 hasRelatedWork W2086783563 @default.
- W2000920261 hasRelatedWork W2122924372 @default.
- W2000920261 hasRelatedWork W2123268069 @default.
- W2000920261 hasRelatedWork W2135746360 @default.
- W2000920261 hasRelatedWork W2150347199 @default.
- W2000920261 hasRelatedWork W2944839787 @default.
- W2000920261 hasRelatedWork W4301423796 @default.
- W2000920261 hasVolume "142" @default.
- W2000920261 isParatext "false" @default.
- W2000920261 isRetracted "false" @default.
- W2000920261 magId "2000920261" @default.
- W2000920261 workType "article" @default.