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.

Alternate Solutions

There are no Alternate Solutions for this problem. Be the first to post one!

Comments

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

Reply to this comment

admin
2013-09-09 22:07:10

test

Reply to this comment

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.

neon37
2010-11-03 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?

Reply to this comment

Post A Comment!

You are replying to:

I just chose (C) because it can\'t be any of the other answers. alliance heroes of the spire

Bare Basic LaTeX Rosetta Stone
LaTeX syntax supported through dollar sign wrappers $, ex., $\alpha^2_0$ produces $\alpha^2_0$ .
type this...	to get...
$\int_0^\infty$	$\int_0^\infty$
$\partial$	$\partial$
$\Rightarrow$	$\Rightarrow$
$\ddot{x},\dot{x}$	$\ddot{x},\dot{x}$
$\sqrt{z}$	$\sqrt{z}$
$\langle my \rangle$	$\langle my \rangle$
$\left( abacadabra \right)_{me}$	$\left( abacadabra \right)_{me}$
$\vec{E}$	$\vec{E}$
$\frac{a}{b}$	$\frac{a}{b}$

The Sidebar Chatbox...
Scroll to see it, or resize your browser to ignore it...

All-Solutions List | Latest Comments | Unanswered Questions (Cries for Help!) |::| About

This site is not affiliated with ETS, nor is it officially endorsed (yet) by ETS. This site is the work of an individual named Yosun Chang. The solutions, sans user comments and ETS questions, are © 2005 by Yosun Chang except where noted. All rights reserved. / The comments appending particular solutions are due to the respective users. / Educational Testing Service, ETS, the ETS logo, Graduate Record Examinations, and GRE are registered trademarks of Educational Testing Service. The examination questions are © 1997 and © 2001 by ETS.

Bare Basic LaTeX Rosetta Stone