Schrödinger's Equation with Forces

Xiao En Wang

According to the energy relationship of the ground state solution of a hydrogen atom using the Schrödinger equation, the kinetic energy of an electron at twice the Bohr radius becomes zero. The electron has zero kinetic energy, which means it is dead, indicating that the energy relationship used in the Schrödinger equation is incorrect. Then, the reasons for both the chaotic energy relationship of the Schrödinger equation and the half frequency problem encountered by Bohr are analyzed. Bohr only considered Coulomb force and established an equation with centrifugal force, but he did not consider Lorentz force. So, the frequency he obtained must be multiplied by 1/2 to match the experimental value. This article also analyzes other issues related to the Schrödinger equation.

G. F. Torres del Castillo, A. S. De la Paz Cota

We show that the solutions of the Schrödinger equation for a free particle are related in a simple manner with the solutions of the Schrödinger equation for a particle in a uniform force field. Making use of this relation we readily obtain the so-called Airy wave packets and the propagator for a particle in a uniform force field.

L.D. LANDAU, Efrat Lifshitz

J. Akande, L. H. Koudahoun, Kolawolé Kêgnidé Damien Adjaï +2 more

In this paper the Schrodinger equation is derived for a dynamical system with exponential-type restoring force function.

L.D. LANDAU, Efrat Lifshitz