An extended class of L{sup 2}-series solutions of the wave equation

Journal Article · Sun May 01 00:00:00 EDT 2005 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2004.11.014· OSTI ID:20690153

Alhaidari, A D ^[1]

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1. Physics Department, King Fahd University of Petroleum and Minerals, Dhahran 31261 (Saudi Arabia)

We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support an infinite tridiagonal matrix representation of the wave operator. The class of solutions obtained as such includes the discrete (for bound states) as well as the continuous (for scattering states) spectrum of the Hamiltonian. The problem translates into finding solutions of the resulting three-term recursion relation for the expansion coefficients of the wavefunction. These are written in terms of orthogonal polynomials, some of which are modified versions of known polynomials. The examples given, which are not exhaustive, include problems in one and three dimensions.

• OSTI ID: 20690153
• Journal Information: Annals of Physics (New York), Vol. 317, Issue 1; Other Information: DOI: 10.1016/j.aop.2004.11.014; PII: S0003-4916(04)00223-4; Copyright (c) 2004 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUND STATE
ENERGY SPECTRA
HAMILTONIANS
INTEGRAL CALCULUS
MATHEMATICAL SOLUTIONS
POLYNOMIALS
RECURSION RELATIONS
SCATTERING
WAVE EQUATIONS
WAVE FUNCTIONS