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## GR0877 Problem 25

PROBLEM STATEMENT: This problem is still being typed.

SOLUTION: (E) The only choice which guarantees that the functions are both normalized $\int_{-\infty}^{+\infty} \psi_i^*(x) \psi_i (x) dx = 1$ and mutually orthogonal $\int_{-\infty}^{+\infty} \psi_i^*(x) \psi_j (x) dx = 0$ for all $i$ and $j$  is (E).

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1. 09.11.2011 at 05:06

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) =$\delta_{ij}$

• 09.11.2011 at 09:45

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.

2. 04.06.2015 at 04:18

To elaborate, answer E has what’s known as the Kronecker delta function, where,
$\delta_{i,j}= \begin{cases} 1, & \text{if } i=j,\\ 0, & \text{if } i\neq j. \end{cases}$

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

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