Other Examples of the Schrödinger Equation

MASSIMO RUDAN

G. F. Torres del Castillo

We present two examples where the Schrödinger equation admits R-separable solutions. In one of them (a particle in a uniform force field) the Schrödinger equation admits separable and R-separable solutions.

David V. George

Song Ling

Contrary to the previous belief, it is found that the time dependent Schrödinger equation is not always reduced to the Hamilton–Jacobi equation in the ℏ→0 limit. An explicit example is given.

Olavo L. Silva Filho, Marcello Ferreira

In this paper, our main objective is to derive the Caldirola-Kanai equation from first principles and present some analytical solutions to it. To do so, we will extend the axioms of the derivation of the Schrödinger equation and, thus, present the derivation of the usual Schrödinger equation, as a means of comparison to its extension. Next, we will present the derivation of the Caldirola-Kanai equation from the same axioms already used to derive the usual Schrödinger equation, now extended to include dissipation; right away, we will give some examples of the application of the Caldirola-Kanai equation (those that are analytically solvable).