Basic Considerations on the Interpretation of Quantum Mechanics A. Einstein (5)

At the end points of the trajectory, the continuous connection to the disappearance of the Ψ-function outside the trajectory is achieved through the requirement that for x=, Ψ=Ϭ. The Ψ-function is then a stationary wave that can be represented within the trajectory by the superposition of 2 harmonic waves traveling in opposite directions: From (1a), we can see that factor A must be the same in both equations so the boundary conditions at the rod ends can be fulfilled. A can be real without loss of generality. b is determined by the Schrödinger equation and determines the mass m. We can consider factor A to be normalized in a known manner. For a fruitful comparison of the example with the corresponding classical problem, we must still state that the ? de Broglie wavelengths are small compared to 1. In the usual way, we now base the explanation of the Ψ-function on Born's probability interpretation: (see figure) This is the probability that the center of gravity coordinate x of the sphere lies within a given interval Ax. It is—apart from an undulating "fine structure," the physical reality of which is fixed—simply const.Ax