PPT Slide
But let us put off worrying about that equation and see what we can do with our knowledge of the wavelength of a “free” particle-- one moving in a region where U(x) is constant.
Inside the box, the particle is free, so the wavelength is h/p, ?(x) = sin kx, but the probability has to be zero outside the box-a boundary condition!! Prob (x) = |?(x)|2 = 0 at edges of the box, and our practice with strings stands us in good stead here, and we see that sin k0 =0 (no information) and at the other end sin kL = 0 -> kL = n? ->
There are lots of other problems we can do by the “locally free” approximation, such as the ball rolling up the hill we mentioned,
Try separation of space and time variables, because we want at first the “stationary states” which do not change in time:
Example of use of the wave equation: tunneling
Email: willis@nevis1.columbia.edu
Home Page: www.nevis.columbia.edu/~willis
Download presentation source