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GR8677 #57
Problem
 GREPhysics.NET Official Solution Alternate Solutions

Quantum Mechanics$\Rightarrow$}Operators

One doesn't really need QM to solve this. Just plug and chug each of the five functions into the following equation,

$-i\hbar \frac{\partial}{\partial x} f = \hbar k f
$

Applying the operator $-i\hbar \frac{\partial}{\partial x}$ to each function included in the choice, one gets:

(A) $i \hbar \sin(k x)$ ... which isn't an eigenfunction

(B) $-i \hbar \cos(k x)$ ... which isn't an eigenfunction

(C) $-\hbar k f$ ... eigenvalue is off by a sign

(D) $\hbar k$ ... this is the wanted eigenvalue!

(E) $-i\hbar k$ ... off by a sign and imaginary term. Moreover, operators representing observables in QM have real eigenvalues.

Alternate Solutions
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ernest21
2019-08-23 02:03:22
I just chose (C) because it can\'t be any of the other answers. alliance heroes of the spire
2013-09-09 22:07:10
test
katajh
2010-10-28 14:26:44
well am i wrong
or i^2 makes -1
so -(-1) gives a positive 1
and says C is the right anwer.
 neon372010-11-03 09:40:22 you are wrong. $i^2 = -1$, but $\frac{\partial e^{-ikx}}{\partial x} = -ik e^{-ikx}$. this multiplied by $-i\hbar$ gives $-\hbar k$. So C is off by a sign. Perhaps you forgot the minus sign from the operator itself?

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