This applet illustrates nonrelativistic quantum mechanical scattering from a one-dimensional square potential well of width L and finite energy depth V>0. The well is located between x=0 and x=L, and the incident wave approaches along the negative x axis.
The energy eigenstates are
where k and are the wavenumbers outside and inside the well, respectively. The eikx term is the incident wave, the R term is the reflected wave, and the T term is the transmitted wave.
The unit of distance is chosen such that the state with k=0 has wavenumber
inside the well.
The coefficients are given by
|R|2 is the reflection coefficient and |T|2 is the transmission coefficient. (They satisfy |R|2+|T|2=1.) The reflection coefficient is given by
This has maxima at those values of k (the scattering resonances) for which
The wavefunction whose probability distribution is animated by the applet has the form
This is a finite sum of energy eigenstates weighted by a Gaussian centered at k0 with width proportional to Dk. The sum runs in equal steps from k0-Dk/2 to k0+Dk/2. A phase factor is included to center the incident wave packet around x=x0 at t=0. The unit of time is chosen such that the frequency is k2/2.
Instructions for use