Akademik Veri Yönetim Sistemi
JOURNAL OF MATHEMATICAL PHYSICS, cilt.46, sa.3, 2005 (SCI-Expanded)
We present an analytical analysis of the two-dimensional Schrodinger equation for two interacting electrons subjected to a homogeneous magnetic field and confined by a two-dimensional external parabolic potential. We have found the general closed-form expression for the eigenstates of the problem and its corresponding eigenenergies for particular values of magnetic field and spatial confinement length. The. mathematical framework is just based on a rigorous solution of the three-term recursion relation among the coefficients that arises from the series solution of biconfluent Heun (BHE) equation, connected with the radial part of the Schrodinger equation for the internal motion. It. is also shown that, by vanishing of Coulomb repulsion strength, the obtained explicit analytical solutions of BHE equation reduces to the well-known polynomials satisfying the associated Laguerre differential equation. Furthermore, in the presence of this interaction, the results are compared with those previously obtained in the literature for first few low-lying states, and are found to be in an exact agreement with them. (C) 2005 American Institute of Physics.