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 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).

If ...

Solution Summary

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.

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