Green's functions through so (2, 1) Lie algebra in nonrelativistic quantum mechanics
Identifieur interne : 002053 ( Main/Exploration ); précédent : 002052; suivant : 002054Green's functions through so (2, 1) Lie algebra in nonrelativistic quantum mechanics
Auteurs : H. Boschi-Filho [Brésil] ; A. N Vaidya [Brésil]Source :
- Annals of Physics [ 0003-4916 ] ; 1991.
English descriptors
- Teeft :
- Academic press, Algebra, Algebraic method, Algebraic technique, Angular part, Asymmetric term, Bessel functions, Commutation relations, Coulomb, Coulomb potentials, Differential equation, Differential operators, Dirac delta function, Dirac electron, Direct product, Dynamical, Dynamical algebra, Dynamical symmetry, Effective hamiltonian, Energy levels, Energy spectrum, Exponential, Free parameter, Function equation, Functions hamiltonian, Hamiltonian, Harmonic, Harmonic oscillator, Integral representation, Inverse square barrier, Laguerre polynomials, Linear combination, Oscillator, Particular case, Particular solution, Phys, Physical system, Point canonical transformation, Resolvent operator, Solvable potentials, Souza dutra, Spherical symmetry, Symmetry condition, Systematic search, Unphysical wave functions, Vaidya, Various values, Wave functions.
Abstract
Abstract: We discuss an algebraic technique to construct the Green's function for systems described by the noncompact so(2, 1) Lie algebra. We show that this technique solves the one-dimensional linear oscillator and Coulomb potentials and also generates particular solutions for other one-dimensional potentials. Then we construct explicitly the Green's function for the three-dimensional oscillator and the three-dimensional Coulomb potential, which are generalizations of the one-dimensional cases, and the Coulomb plus an Aharonov-Bohm potential. We discuss the dynamical algebra involved in each case and also find their wave functions and bound state spectra. Finally we introduce a point canonical transformation in the generators of so(2, 1) Lie algebra, show that this procedure permits us to solve the one-dimensional Morse potential in addition to the previous cases, and construct its Green's function and find its energy spectrum and wave functions.
Url:
DOI: 10.1016/0003-4916(91)90370-N
Affiliations:
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We show that this technique solves the one-dimensional linear oscillator and Coulomb potentials and also generates particular solutions for other one-dimensional potentials. Then we construct explicitly the Green's function for the three-dimensional oscillator and the three-dimensional Coulomb potential, which are generalizations of the one-dimensional cases, and the Coulomb plus an Aharonov-Bohm potential. We discuss the dynamical algebra involved in each case and also find their wave functions and bound state spectra. Finally we introduce a point canonical transformation in the generators of so(2, 1) Lie algebra, show that this procedure permits us to solve the one-dimensional Morse potential in addition to the previous cases, and construct its Green's function and find its energy spectrum and wave functions.</div></front></TEI><affiliations><list><country><li>Brésil</li></country><region><li>État de Rio de Janeiro</li><li>État de São Paulo</li></region><settlement><li>Rio de Janeiro</li></settlement></list><tree><country name="Brésil"><region name="État de Rio de Janeiro"><name sortKey="Boschi Filho, H" sort="Boschi Filho, H" uniqKey="Boschi Filho H" first="H" last="Boschi-Filho">H. Boschi-Filho</name></region><name sortKey="Boschi Filho, H" sort="Boschi Filho, H" uniqKey="Boschi Filho H" first="H" last="Boschi-Filho">H. Boschi-Filho</name><name sortKey="Vaidya, A N" sort="Vaidya, A N" uniqKey="Vaidya A" first="A. N" last="Vaidya">A. N Vaidya</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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