GREPhysics.NET: GR8677 #57

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,

$-i\hbar \frac{\partial}{\partial x} f = \hbar k f<br />$

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.

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