Journal Title, Volume, Page:

Int. J. Mod. Phys. C 18, 1571
Year of Publication:

2007
Preferred Abstract (Original):

Utilizing an appropriate ansatz to the wave function, we
reproduce the exact bound-state solutions of the radial Schrödinger
equation to various exactly solvable sextic anharmonic oscillator and
confining perturbed Coulomb models in D-dimensions. We show that the
perturbed Coulomb problem with eigenvalue E can be transformed to a
sextic anharmonic oscillator problem with eigenvalue .
We also check the explicit relevance of these two related problems in
higher-space dimensions. It is shown that exact solutions of these
potentials exist when their coupling parameters with k = D +2ℓ appearing
in the wave equation satisfy certain constraints.

Journal Title, Volume, Page:

J. Chem. Phys. 102, 4919 (1995)
Year of Publication:

1995
Preferred Abstract (Original):

In Z-dependent perturbation theory, the lowest-order wave functions for a polyatomic molecule are not only independent of the nuclear charges, but also of the total number of nuclear centers and electrons in the molecule. The complexity of the problem is then determined by the highest order retained in the calculation. Choosing the simplest possible unperturbed Hamiltonian, we describe an n-electron, m-center polyatomic molecule as n ‘‘hydrogenic’’ electrons on a single center perturbed by electron–electron and electron–nucleus Coulomb interactions. With this H0 , the first-order wave function for any polyatomic molecule will be a sum of products of hydrogenic orbitals with either two-electron, one-center or one-electron, two-center first-order wave functions. These first-order wave functions are obtained from calculations on He-like and H2 1-like systems. Similarly, the nth-order wave function decouples so that the most complex terms are just the nth-order wave functions of all the p-electron, q-center subsystems (p1q5n12) contained in the molecule. We illustrate applications of this method with some results, complete through third order in the energy, for H31-like molecules. These are compared with accurate variational results available in the literature. We conclude that, through this order, this perturbation approach is capable of yielding results comparable in accuracy to variational calculations of moderate complexity. The ease and efficiency with which such results can be obtained suggests that this method would be useful for generating detailed potential energy surfaces for polyatomic molecules. © 1995 American Institute of Physics.