Two Interacting Wells
The two wells are identical to the ones in Section 1 except that they are
Section 2 Exercises:
- What is the width of the barrier separating the two wells?
- What are the energies of the first six eigenstates? Are any of them
degenerate to the accuracy of the measurement?
- What is the parity of this lowest lying state?
The Schroedinger equation relates the second derivative of the wave function
to the energy times the wave function. Mathematically speaking, the second
derivative is a measure of the curvature of a function. A line has zero
curvature and a parabola has a constant curvature.
- Which of the lowest two states has the greatest overall curvature?
Does it correspond to the state with the largest binding energy?
- Is the probability of finding the electron halfway between the two wells
zero for either of the two lowest states? How might your answer to
this question be used to interpret your result in #3 above?
- Use the increase in energy splitting between pairs as the quantum number n
increases to make a general statement about the curvature of the wave
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