I am given three unnormalized wavefunctions for the system:
psi(x) = 100e^x for x<-4
psi(x) = 0.73 cos[(pi)x/40] for-4<x<4
psi(x) = 100e^-x for x>4
I need to determine the probability of the wavefunction vs. x for this system from x=-10 to x=10 so that I can plot it. I have to comment on the probability of finding the particle outside of the box (x<-4 or x>4). Then I need to find the average kinetic energy of the particle between -4 and 4 using the kinetic energy operator and integral tables (Use the unnormalized function). Then I need to normalize the wavefunction in the region between -4 and 4.
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The solution is attached below in two files. The files are identical in content, only differ in format. The first is in MS Word XP Format, while the other is in Adobe pdf format. Therefore, you can choose the format that is most suitable to you.
The last question is pretty ambiguous.
If you need to normalize the wave function only at -4<x<4 disregarding the rest, I answered that in the last part of my answer (this is making the problem an infinite well problem).
This solution is provided in approximately 219 words. It discusses wave function conditions and writes equations and continuity for the unnormalized functions. A diagram of the normalized wave function is provided along with the probability.