Phys 2D soln5

Phys 2D soln5 - 1a To determine whether a finite square...

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Unformatted text preview: 1a To determine whether a finite square well of depth U is “deep” or “shallow”, U should be compared to ~ 2 / 2 mL 2 . I’ll call this energy scale E ∞ for short. Notice that E ∞ roughly the energy of a particle in the ground state of the infinite square well. When U E ∞ , the depth of well is large compared to the energy of the particle just like in infinite square well case. So, the system should behave like the infinite square well in this case. In the opposite case, U E ∞ , the well is shallow and there is no reason to expect the system will behave in the same way as the infinite square well. 1b In both cases, the probability to find the particle outside of the well decays exponentially with distance away from the well. In a very deep well this decay is strong, and conse- quentially the particle will almost always be found in the well. In a very shallow well, the exponential damping is much weaker. This gives the particle a decent chance of being found outside of the well, but best chance of the finding the particle is still in the well.found outside of the well, but best chance of the finding the particle is still in the well....
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Phys 2D soln5 - 1a To determine whether a finite square...

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