Question

Please answer a,b and c.

Now, consider a 1-d infinite square well of width a, between x = 0 and a, such that V(x) = 0 for 0<x<a and too elsewhere. A perturbation is then added to it so that V(x) = V. for 0 <x <a/2, and the same as before elsewhere. In other words, a flat bump of width a/2 and height V. in the left half of the well. (a) (5 pts) Carefully sketch the potential and indicate all of its relevant parameters. (b) (15 pts) Write down the complete expressions for the first order energy correction En. Evaluate the integrals. (Hint: use properties of the eigenfunctions!) (c) (10 pts) Write down the complete expressions (that is, wave functions, integrals, variables, limits, etc.) for calculating the 1st order correction in to the wave functions and 2nd order energy correction E2.

Answer 1

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