Please be legible and thorough. please be detailed with your explanations. thank you very much.
Q: Solve the infinite potential well problem for a symmetric well. That is, the potential energy function is given by the following:
-a CO r I 2 -a 2 V(r)={ 0 .rs ss > a CO < 2 Or graphically: KV(x) 1 III a/2
your solution should give the following: (a) normalized eigenfunctions (b) eigenvalues hints: follow the same procedure as done in the text, section 2.2 of griffiths. the only significant difference is the boundary conditions. you should also note that unlike the version in the text(called the asymmetric well) this well is symmetric about the origin and hence shows reflection symmetry: V(.x)=V(-x). As a result, your eigenfunctions must be either even or odd under the same reflection operation. This means you should have two sets of eigenfunctions, one even and the other odd under x inversion. Make sure you see this. X