A Note on the General Solution of Schrödinger's Equation and the Uncertainty Principle

Abstract

It is shown that the general solution of Schrödinger's equation in one dimension for a given energy can be written in a form representing two beams travelling in opposite directions with the classical velocity. This permits an interpretation of the uncertainty principle in which an electron in a conservative field, with a definite energy, has also a definite speed, but its direction of motion is indeterminate. In regions in which the classical velocity is imaginary this interpretation becomes indefinite. A brief consideration is given to the generalization to three dimensions.