Rechenberg, in their classic study, in which Schrödinger and wave mechanics was given more space than any other subject (close to a thousand pages!), discuss his time-dependent equation and note its significance, especially its introduction of the complex wave function, their analysis is brief and does not address the deeper physical and philosophical aspects of this equation (Mehra and Rechenberg 2001, v. Section 5.4 comments on Dirac’s equation in connection with Schrödinger’s time-dependent equation, which is the nonrelativistic limit of Dirac’s equation. Section 5.3 considers Schrödinger’s derivation of his time-dependent equation. Section 5.2 revisits Schrödinger’s derivation of his time-independent equation.
The present approach to his time-dependent equation is new because it focuses on those features of the equation that emerge against Schrödinger’s own grain. The time-dependent equation and its derivation have been given less attention in the literature, in contrast to his time-independent equation and its derivation, which, along with Schrödinger’s program for wave mechanics, have been discussed extensively. This chapter discusses Schrödinger’s time-dependent equation and its mathematical features.
