A New Derivation of the Time-Dependent Schrödinger Equation from Wave and Matrix Mechanics

Abstract

An alternative method is proposed for deriving the time dependent Schroedinger equation from the pictures of wave and matrix mechanics. The derivation is of a mixed classical quantum character, since time is treated as a classical variable, thus avoiding any controversy over its meaning in quantum mechanics. The derivation method proposed in this paper requires no ad hoc assumption and avoids going through a second-order differential equation that can be reduced to the well known time-dependent Schroedinger equation only postulating a complex wavefunction with an exponential time dependence, as did by Schroedinger in its original paper of 1926.

6 pages. Advances in Physics Theories and Applications, Vol. 43 (2015) ISSN 2224-719X (Paper) ISSN 2225-0638 (Online) Vol 43, 2015 Advances in Physics Theories and Applications - Vol 43, 2015