Question

Consider a set of wave functions vi(x). Which of the following conditions guarantees that the functions are normalized and mutually orthogonal? (The indices i and j take on the values in the set {1, 2, ...,n}.) (A) V (x)v; (x) = 0 (B) y (x)y; (x) = 1 (C) vi(x)\;(x)dx = 0 (D) { vi (x)y;(x)dx E) (x)} (x) dx = 8

Please show all your work. I'm studying for the physics GRE so it would be very helpful. Thank you!

Answer 1

This problem can be solved using the definition of orthogonality and normalization together with the definition of the kronecker delta function. The answer turns out to be option (E). Detailed solution given below. Ask me if you have any doubts. Feedback will be helpful.


This shows that wer when izj, the inner product becomes 1 This is exactly the property of kronecker data delta function, 0 2 izj 1 lias Sij Hence both both orthogonality and normalization can be summarized using Sij Y; (ujt V; (4) du = dij This is option no. (E)