The Markov processes of Schr�dinger

Robert Warren Finkel

Robert G. Cawley

HU Xian-quan

Most of Schrdinger equations in quantum mechanics haven't analytic solutions except the problems of well with infinite depth,one-dimensional linear harmonic oscillator and Coulomb's potential as well as three-dimensional isotropic harmonic oscillator.These Schrdinger equations include the various equations in the non-spherical ring shaped oscillator potential that haven't analytic solutions. We can only solve these problems approximately in our research activities, but the solving process of these problems is often exceptional complex.The limitation handicaps us to lucubrate the idiographic problems.This paper adopts NU Method(A.F.Nikiforov-V.B.Uvarov Method) to solve the angular equation of the Schrdinger equation in the non-spherical ring shaped oscillator potential V(r,θ)=μω2r2/2+2α/(2μr2)+2βcosθ/(2μr2sin2θ).We decompose the Schrdinger equation in the non-spherical ring shaped oscillator potential step by step until we obtains the analytic solutions of the equation,thus we obtain the analytic solution of the angular eigenfunction,and simplify the process of solutions.Moreover,this paper adopts special functions in the radial equation at the same time to broaden our study in solving the Schrdinger equations.

Crispin W. Gardiner, P. Zoller

Nikhil Singh

Erwin Schr & #214;dinger is considered one of the founding father of quantum mechanics. Schr & #214;dinger's equation is fundamental of understanding Quantum Mechanics. Laws of Newtonian system don't work in quantum system. In this Research paper I have discussed brief overview on Schr & #214;dinger's wave equation.

Burkhard Kümmerer