Origin of the Schrödinger Equation

Baxter H. Armstrong, Edwin Albert Power

It is shown that the condition of finiteness at the origin, usually imposed on solutions to the nonrelativistic Schrödinger equation for the hydrogen atom (and some other systems) is not necessary. The quadratically integrable l = 0 “anomalous” solution which is usually excluded in this fashion is not a solution to the Schrödinger equation at the origin, and consequently does not need to be excluded by a boundary or other type condition. The relativistic generalization through the Dirac equation of this anomalous solution is not quadratically integrable. The solution generalized according to the relativistic Schrödinger equation is quadratically integrable and obeys the equation at the origin. Consequently, a boundary or other type condition may still be needed in a general relativistic theory.

Thomas B. Andrews

Kao Xiujuan

Discussed the origin of Schrodinger equation.Although Schrodinger equation is a analoging equation,we can find the result according with the fact when we apply it to describe the electron..It becomes the theoretical basic of quantum mechanics.

Doug Jensen

Robert Wieser, Chan‐Ho Yang

Abstract The missing derivation of the time-dependent Schrödinger equation following Schrödinger’s original description of the time-independent Schrödinger equation. Also, this description is extended to derive the Caldirola-Kanai, the Schuch-Schrödinger, and the Gisin-Schrödinger equation. In the second part, the Gisin-Schrödinger equation will be derived once more using the Ito formalism of stochastic differential equations. Furthermore, we discuss the extension to larger spin-system using the cluster mean-field theory.

H. N. Ioannidou