Finite Well: The goal here is to find the energies for a finite well whose width L is 4 an...

Finite Well: The goal here is to find the energies for a finite well whose width L is 4 and whose depth U0 is 5 in the simple system of units discussed above. To exploit symmetry, assume that the finite well extends not from x = 0 to x = 4, but from x = -2 to x =+2. For U(x), the function 2.5*sign(x^2 - 4) + 2.5 can be adapted to almost any computer, (a) Plot this U(x). (b) For Δx, use 0.001. Now, following the above guidelines on choosing if ψ(0) and ψ(Δx), test both odd and even functions at different trial values of E by finding tp at all positive multiples of Δx out to x = 4 and plotting the results. Note that because of the functions' symmetries, there is no need to plot negative values of x. Find four allowed energies, (c) What tells you that an energy is correct? (d) Using the definitions of k and a, the finite well energy quantization condition, given in equation (5-22), can be written

It can't be solved exactly, but do your values satisfy it reasonably well?