## GR0877 Problem 25

**PROBLEM STATEMENT**: *This problem is still being typed*.

**SOLUTION**: (**E**) The only choice which guarantees that the functions are both normalized and mutually orthogonal for all and is (E).

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To elaborate, (a) and (b) don’t make any sense and can be eliminated, while (c) is the condition for orthogonality, (d) is the condition for normalization, and (e) is by definition the condition for functions that are normalized and mutually orthogonal AKA orthonormal.

OR in Dirac notation if you prefer, (c) =0, (d) =1, (e) =

To write latex formulas, please use this notation:

DOLLARSIGNlatex your_formulaDOLLARSIGN

without space between dollar sign and the word ‘latex’. I’ve edited your comments.

To elaborate, answer E has what’s known as the Kronecker delta function, where,

Which satisfies both the wave function equaling 0 and 1, depending on i,j