Could Planck-Einstein relation be applied to matter waves?

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  • Thread starter Haorong Wu
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Summary:

Could Planck-Einstein relation be applied to matter waves?
My friend gave me some statements which are wrong, but I could not tell why they are wrong.

He wrote,

Since ##\omega = \frac E \hbar = \frac {\hbar k^2} {2m} = k v##, then##p=\hbar k =2mv##.

I guess that ##E =\hbar \omega## may only appied to photons, not matter waves. Is that correct?
 

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  • #2
Demystifier
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##E=\hbar\omega## is true for both photons and matter waves. However, ##E=\hbar^2k^2/2m## is correct only for non-relativistic matter waves. On the other hand, ##E=\hbar k v## is correct only for photons, for which ##v=c##.
 
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  • #3
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##E=\hbar\omega## is true for both photons and matter waves. However, ##E=\hbar^2k^2/2m## is correct only for non-relativistic matter waves. On the other hand, ##E=\hbar k v## is correct only for photons, for which ##v=c##.
Thanks, Demystifier. But I still can not understand it clearly.

Meanwhile, could the problem be the velocity? The velocity for ##p= mv## should be the group velocity of the matter wave which is ##v=\frac {dw} {dk}##. If so, I can get a proper answer then.
 
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Demystifier
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The velocity for ##p= mv## should be the group velocity of the matter wave which is ##v=\frac {dw} {dk}##. If so, I can get a proper answer then.
That's OK, but you should be careful about what do you take for the function ##\omega(k)##. For photons it is ##\omega=ck##, while for non-relativistic matter it is ##\omega=\hbar k^2/2m##.
 
  • #5
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That's OK, but you should be careful about what do you take for the function ##\omega(k)##. For photons it is ##\omega=ck##, while for non-relativistic matter it is ##\omega=\hbar k^2/2m##.
Thanks, Demystifier. I will be careful about that.
 

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