%0 Journal Article %1 springerlink:10.1007/s10910-012-0055-1 %A Zhang, Min-Cang %D 2012 %I Springer Netherlands %J Journal of Mathematical Chemistry %K basis equation mechanics physics quantum schrodinger solution tridiagonal %N 10 %P 2659-2670 %R 10.1007/s10910-012-0055-1 %T Tridiagonal treatment for the Schrödinger equation with a noncentral electric dipole ring-shaped potential %U http://dx.doi.org/10.1007/s10910-012-0055-1 %V 50 %X A noncentral potential is proposed in which the noncentral electric dipole and a ring-shaped component $$^2þeta/r^2\sin^2þeta$$ are included. The exactly complete solutions of the Schrödinger equation with this potential is investigated by working in a complete square integrable basis that supports an infinite tridiagonal matrix representation of the wave operator. The solutions obtained are for all energies, the discrete (for bound states) as well as the continuous (for scattering states). The expansion coefficients of the wavefunctions (both angular and radial) are written in terms of orthogonal polynomials satisfying three-term recursion relation. The discrete spectrum of the bound states is obtained by diagonalization of the radial recursion relation.

@article{springerlink:10.1007/s10910-012-0055-1, abstract = {A noncentral potential is proposed in which the noncentral electric dipole and a ring-shaped component $${\cos ^{2}\theta/r^{2}\sin^{2}\theta}$$ are included. The exactly complete solutions of the Schrödinger equation with this potential is investigated by working in a complete square integrable basis that supports an infinite tridiagonal matrix representation of the wave operator. The solutions obtained are for all energies, the discrete (for bound states) as well as the continuous (for scattering states). The expansion coefficients of the wavefunctions (both angular and radial) are written in terms of orthogonal polynomials satisfying three-term recursion relation. The discrete spectrum of the bound states is obtained by diagonalization of the radial recursion relation.}, added-at = {2012-10-27T13:52:21.000+0200}, affiliation = {College of Physics and Information Technology, Shaanxi Normal University, Xi’an, 710062 People’s Republic of China}, author = {Zhang, Min-Cang}, biburl = {https://www.bibsonomy.org/bibtex/22f010ef5e312fb3282c77a16c552150f/drmatusek}, doi = {10.1007/s10910-012-0055-1}, interhash = {b96852be799ed88891b0402de382caf4}, intrahash = {2f010ef5e312fb3282c77a16c552150f}, issn = {0259-9791}, journal = {Journal of Mathematical Chemistry}, keyword = {Chemistry and Materials Science}, keywords = {basis equation mechanics physics quantum schrodinger solution tridiagonal}, month = nov, number = 10, pages = {2659-2670}, publisher = {Springer Netherlands}, timestamp = {2012-12-06T03:33:50.000+0100}, title = {Tridiagonal treatment for the Schrödinger equation with a noncentral electric dipole ring-shaped potential}, url = {http://dx.doi.org/10.1007/s10910-012-0055-1}, volume = 50, year = 2012 }