Consider a particle in an infinite square well, but instead of having the well from 0 to L as we have done in the past, it is now centered at 0 and the walls are at x = −L/2 and x = L/2.
(a) Draw the first four energy eigenstates of this well.
(b) Write the eigenfunctions for each of these eigenstates.
(c) What are the energy eigenvalues for this system?
(d) Can you find a general expression for the energy eigenstates for this well? (Hint: you should have a different form for even and odd solutions) (e) If instead, the well were from x = −L to x = L, how would these expressions change? Would the energy eigenvalues change? (And if so, how?)
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