Consider the potential (V(x) V 0 e alpha x 2 ) Calculate perturbatively the first two terms in the solutions ( psi 1 (x) left( sim e i k x ight ) at (x infty ), incoming) and ( psi 2 (x) left( sim e i k x ight ) at (x infty ), outgoing), if (E leq V 0 ) ...

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Consider the potential (V(x)=V_{0} e^{-alpha x^{2}}). Calculate perturbatively the first two terms in the solutions (psi_{1}(x)left(sim e^{i

Question:

Consider the potential \(V(x)=V_{0} e^{-\alpha x^{2}}\). Calculate perturbatively the first two terms in the solutions \(\psi_{1}(x)\left(\sim e^{i k x}\right.\) at \(x=-\infty\), incoming) and \(\psi_{2}(x)\left(\sim e^{i k x}\right.\) at \(x=+\infty\), outgoing), if \(E \leq V_{0}\).

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