Double Stern-Gerlach Experiment and Related Collision Phenomena

Abstract

The theory of the double Stern-Gerlach experiment is developed where the rate of rotation has a maximum at $t=0\mathrm{}$ and goes gradually to zero at $t=\pm \infty$. The negative results of the experiments of Phipps and Stern are completely accounted for. The same analysis is applied to those collision phenomena where only two quantum states need be considered, and where their difference of energy, $\Delta E$, is so much smaller than the relative kinetic energy of the two systems that the positions of the centers of gravity of the two systems may be regarded as time parameters. If $f\left(t\right)=\frac{2\pi }{h}$ times the matrix element of the perturbation, and if $A=\int {-\infty }^{\infty }f\left(t\right)\mathrm{dt}$, then the transition probability is ${\left|\frac{sinA}{A}\int {-\infty }^{\infty }f\left(t\right)\mathrm{}{e}^{2\pi i\left(\frac{\Delta E}{h}\right)t}\mathrm{dt}\right|}^2$ for the cases investigated, and this probably holds for all experimental cases.