GREPhysics.NET: GR9277 #1

GR9277 #1

Problem

GREPhysics.NET Official Solution

\prob{1}
The wave function of a particle is $e^{i(kx-\omega t)}$ where x is distance, t is time, and k and $\omega$ are positive real numbers. The x-component of the momentum of the particle is

0
$\hbar\omega$
$\hbar k$
$\frac{\hbar\omega}{c}$
$\frac{\hbar k}{\omega}$

Quantum Mechanics $\Rightarrow$ }Momentum Operator

$\hat{p}=\frac{\hbar}{i}\frac{\partial}{\partial x}\psi \Rightarrow p \psi = \hbar k \psi <br />$

Alternate Solutions

casseverhart13 2019-07-04 10:57:43	Thanks for your post! electrical contactor\r\n Reply to this comment
tera 2006-08-21 02:14:34	You can get the result by dimentional analysis Reply to this comment

Comments

casseverhart13
2019-07-04 10:57:43

Thanks for your post! electrical contactor\r\n

Reply to this comment

deepblue
2013-03-04 18:35:26

This website is great.

I was wondering if there was a possible miscalculation.

It appears using the momentum operator normally defined you would have

-(i)*(i)hk which leads to an imaginary number times an imaginary number which is -1 .

So you have - [(i)*(i)] = (-)(-1)hk. So you get answer (C) which is just hk.
=================================================
(My point is the author divided by (i) in the definition of the momentum operator instead of multipling the two imaginary numbers)

zeper
2013-03-09 09:11:39

no there is no mistake...1/i means -i...which is the same notation you mensioned.

Reply to this comment

grep
2006-10-30 13:28:58

You can also recognize that the wave function is just a standard transverse wave (like a light wave) for which de Broglie tells us h=lambda*p and the propagation number tells us k=2 pi/lambda

roofsing
2010-06-21 23:37:57

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grep
2006-10-03 12:37:48

Oops, I meant it also leaves choice D

BerkeleyEric
2010-05-31 15:18:12

(D) actually gives units of kg * m/s^2, not kg * m^2/s as needed. (A) cannot be eliminated from dimensional analysis, but from physical intuition we know that a wave traveling in the x-direction should have momentum in the x-direction.

Reply to this comment

grep
2006-08-28 13:07:27

Hmm, doesn't dimensional analysis leave C as a possible choice? (or A for that matter)

gina4eva
2011-11-10 18:10:14

but isn't c the answer?

Reply to this comment

tera
2006-08-21 02:14:34

You can get the result by dimentional analysis

alemsalem
2010-09-24 08:30:20

the units for choice D also work but we dont know that the particle is moving with speed of light.

Quark
2011-10-25 12:04:21

More accurately, the particle can't be moving at the speed of light.

myscifilullaby1
2012-03-08 17:32:19

indeed! dimensional analysis gives two possibilities, A & C. When you use the momentum operator, you get C as the final answer.

Reply to this comment

gottlob
2006-06-13 12:18:50

I am a physics teacher from Greece and am trying to download the gre.pdf forms of the gre tests. I have downloaded the GRE0177 but i can't get the others (GRE9677, GRE9277 etc. My e-mail is nchalk@phs.uoa.gr. Please, if any one can sent me, or give me information about, the tests i would be gratefull to him.

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