Wave Function, Schrödinger Equation

Kristiana Nathalia Wea, Suparmi Suparmi, C. Cari +1 more

The solution of the Schrodinger equation with the physical potential is important part in quantum mechanics. The anharmonic potential is one of the physical potential that is interesting to be explored. Many methods have been developed to solve the Schrodinger equation. The Ansatz wave function method is one of the many methods that used to solve the Schrodinger equation. The Ansatz wave function method was used to solve the radial part of Schrodinger Equation. In this study we present the solution of the radial part Schrodinger equation in D-dimensional system with potential V(r)=ar2+br+cr-1+dr-2+er-3+fr-4. The important part in Ansatz wave function method is to determine the wave function Ansatz corresponding to the shape of the anharmonic potential that used. The Ansatz wave function determined by using supersymmetric approximation. By substituting the wave function Ansatz into Schrodinger equation and using algebraic we obtain the radial eigenfunction and the energy, and then the eigenfunction visualized.

Jean-Louis Basdevant

Declan Traill

The Schrodinger equation is not Lorentz Invariant, so it cannot be applied to the wave functions of moving particles. However, the Classical Wave Equation is Lorentz Invariant and is also satisfied by particle wave functions. By using this knowledge, a Lorentz Invariant form of the Schrodinger equation can be developed that can be applied to the wave functions of moving particles.

Professor Jean-Louis Basdevant

Isaac Shnaid

According to classical non-relativistic Schrödinger equation, any local perturbation of wave function instantaneously affects all infinite region, because this equation is of parabolic type, and its solutions demonstrate infinite speed of perturbations propagation. From physical point of view, this feature of Schrödinger equation solutions is questionable. According to relativistic quantum mechanics, the perturbations propagate with speed of light. However when appropriate mathematical procedures are applied to Dirac relativistic quantum equation with finite speed of the wave function perturbations propagation, only classical Schrödinger equation predicting infinite speed of the wave function perturbations propagation is obtained. Thus, in non-relativistic quantum mechanics the problem persists. In my work modified non-relativistic Schrödinger equation is formulated. It is also of parabolic type, but its solutions predict finite speed of the wave function perturbations propagation. Properties of modified Schrödinger equation solutions are studied. I show that results of classical Davisson-Germer experiments with electron waves diffraction support developed theoretical concept of modified Schrödinger equation, and predict that speed of the wave function perturbations propagation has order of magnitude of speed of light.