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  GR9277 #1
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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

  1. 0
  2. $\hbar\omega$
  3. $\hbar k$
  4. $\frac{\hbar\omega}{c}$
  5. $\frac{\hbar k}{\omega}$

Quantum Mechanics}Momentum Operator

See below for user comments and alternate solutions! See below for user comments and alternate solutions!
Alternate Solutions
2006-08-21 02:14:34
You can get the result by dimentional analysisAlternate Solution - Unverified
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)
2013-03-09 09:11:39
no there is no mistake...1/i means -i...which is the same notation you mensioned.
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
2010-06-21 23:37:57

2006-10-03 12:37:48
Oops, I meant it also leaves choice D
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.
2006-08-28 13:07:27
Hmm, doesn't dimensional analysis leave C as a possible choice? (or A for that matter)
2011-11-10 18:10:14
but isn't c the answer?
2006-08-21 02:14:34
You can get the result by dimentional analysis
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.
2011-10-25 12:04:21
More accurately, the particle can't be moving at the speed of light.
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.
Alternate Solution - Unverified
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 Please, if any one can sent me, or give me information about, the tests i would be gratefull to him.NEC

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