Superposition Of The Potential Power Function Exact Solutions Of The Schrodinger Equation

This paper briefly discusses the solution of Schrodinger equation approximate analytical solutions and numerical solution method, we know in addition to hydrogen atom and a few, such as harmonic oscillator potential, the majority of the corresponding potential energy levels and wave functions are not the analytical solution is given. Various forms of power, potential and justified in the form of potential in many areas of physics of a wide range of applications, people transform function, the method of SU(2), supersymmetric variational method, numerical calculation method and the method of raising and lowering operators, and other methods of such potential is more complex forms of energy, wave functions and other properties were discussed. This paper ring oscillator (RSO) potential function in spherical coordinates in the Schr?dinger equation equation using separation of variables method, the radial angle to the equation and the equation. And through variable substitution and the substitution function, the final solution convergence hypergeometric equation, wave functions of the standard conditions of the spectrum are given precise equation, and then from the orthogonal generalized Laguerre polynomial of a given return normalization of the wave function; And circumstances discuss V ( r )= ar 2 + br 4 + cr6 in this paper three-dimensional non-spherical harmonic oscillator potential energy levels and wave function, the method used was the radial wave function will be launched for the exponential function and the product of polynomial function by polynomial coefficients between the recursive , then use the relationship to system-level and wave function, A low-power polynomial function for example( p = 0,1,2), are given corresponding to the specific energy levels and wave functions of exact solutions; Finally Nikiforov-Uvarov (NU) method in the RSO and non-spherical harmonic Oscillator stack potential under the conditions of reduced-order super geometric equations to the general equation, a solution based on the second-order linear differential equations to determine the accuracy of the Schr?dinger equation, Accurately display a new ring of non-harmonic oscillator potential of the Schrodinger equation bound state solution, Jacobian polynomials can be found that the angle of the wave function, and, generalized Laguerre polynomial to express Drive Solutions to the wave function. Therefore, the study Coulomb potential superimposed on the new ring-type non-harmonic oscillator potential is practicable, for the enrichment and development of quantum theory has important significance.At the same time this paper is on two power with two inverse power potential function under the conditions of superposition radial Schrodinger equation exact solution.A singular point of the neighborhood near Solution Series and the asymptotic solution obtained by combining indicators s power function, as well as the coefficient of restraint, and by comparative law by power series coefficient for the potential function of V ( r)= a1r6 +a2r2+a3r?4 +a4r?6radial Schrodinger Equation of state for wave function and the corresponding exact solution of the energy level structure, and use tools such as MATLAB software to wave function maps.