In previous studies, by the methods of wave mechanics, of one-dimensional motion of particles in cases in which there are intervals in which the value of the potential energy function $V\left(x\right)\mathrm{}$ exceeds the value of the total energy $E$, attention has been confined to wave functions of the form $f(x, E)\exp (-\frac{2\pi \mathrm{iEt}}{h})$. In the present note wave packets are considered, instead of these trains of waves.

The function $V\left(x\right)\mathrm{}$ is taken as follows: $\left\{V\right(x)\mathrm{},=0\mathrm{} \mathrm{for} x<\mathrm{}0\mathrm{} \mathrm{and}\mathrm{for} x>a,\}\{=V_0>0\mathrm{} \mathrm{for} 0<x<a.\mathrm{}\}$ A wave function is set up which initially represents a wave packet moving toward the point $x=0\mathrm{}$ from the left. The separation of the incident packet into a reflected packet and a transmitted packet is studied. It is found that the transmitted packet appears at the point $x=a$ at about the time at which the incident packet reaches the point $x=0\mathrm{}$, so that there is no appreciable delay in the transmission of the packet through the barrier.

• Received 14 January 1932

DOI:https://doi.org/10.1103/PhysRev.40.621