The Time-Independent Schrödinger Equation

Abstract

It is important to remember that the Schrödinger equation, similar to the principal thermodynamic laws, cannot be derived from the general principles of physics. It is true that we can proceed from the classical law of conservation of energy and, through a number of modifications (some of them inconceivable from the point of view of classical mechanics), arrive at the Schrödinger equation (“derive it”). However, this procedure does not possess the character of derivation by deduction that is considered normal in classical physics. The only method of determining whether the equation obtained has physical significance, i.e. whether it gives a true picture of the real behaviour of particles, will lie in comparison of values for quantities calculated using this equation with experimentally obtained values.