Analytic solution of the wave equation for an electron in the field of a molecule with an electric dipole moment

Journal Article · Tue Jul 15 00:00:00 EDT 2008 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2007.12.005· OSTI ID:21163716

Alhaidari, A D ^[1]

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1. Shura Council, Riyadh 11212 (Saudi Arabia)

We relax the usual diagonal constraint on the matrix representation of the eigenvalue wave equation by allowing it to be tridiagonal. This results in a larger representation space that incorporates an analytic solution for the non-central electric dipole potential cos{theta}/r{sup 2}, which was believed not to belong to the class of exactly solvable potentials. Therefore, we were able to obtain a closed form solution of the three-dimensional time-independent Schroedinger equation for a charged particle in the field of a point electric dipole that could carry a nonzero net charge. This problem models the interaction of an electron with a molecule (neutral or ionized) that has a permanent electric dipole moment. The solution is written as a series in a basis composed of special functions that support a tridiagonal matrix representation for the angular and radial components of the wave operator. Moreover, this solution is for all energies, the discrete (for bound states) as well as the continuous (for scattering states). The expansion coefficients of the radial and angular components of the wavefunction are written in terms of orthogonal polynomials satisfying three-term recursion relations. For the Coulomb-free case, where the molecule is neutral, we calculate critical values for its dipole moment below which no electron capture is allowed. These critical values are obtained not only for the ground state, where it agrees with already known results, but also for excited states as well.

• OSTI ID: 21163716
• Journal Information: Annals of Physics (New York), Vol. 323, Issue 7; Other Information: DOI: 10.1016/j.aop.2007.12.005; PII: S0003-4916(07)00191-1; Copyright (c) 2007 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
ANALYTICAL SOLUTION
BOUND STATE
CHARGED PARTICLES
EIGENVALUES
ELECTRIC DIPOLE MOMENTS
ELECTRIC DIPOLES
ELECTRON CAPTURE
ELECTRON-MOLECULE COLLISIONS
ELECTRONS
EXACT SOLUTIONS
EXCITED STATES
GROUND STATES
MATRICES
POLYNOMIALS
POTENTIALS
RECURSION RELATIONS
SCATTERING
SCHROEDINGER EQUATION
THREE-DIMENSIONAL CALCULATIONS
WAVE FUNCTIONS