A Please help me understand this HO energy in He4 gas

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Summary
The result of angular frequency deduced from Eq 1.8 is quite confusing to me. Can some one walk me through it please?

Thank you
0C815455-2F07-4141-BFED-574E862BC6E3.jpeg
 

dRic2

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It seems to me the author used the relation ##\omega^2 = \frac k m## for the frequency of an harmonic oscillator, where -in this case- ##k = \phi_p## and ##m = \frac 1 {\rho p^2}##.
 
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It seems to me the author used the relation ##\omega^2 = \frac k m## for the frequency of an harmonic oscillator, where -in this case- ##k = \phi_p## and ##m = \frac 1 {\rho p^2}##.
No, I don’t think so
 

dRic2

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561
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Why not ? It looks like the total energy of an HO... BTW I'm sorry but that's the only thing I could think of
 
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Why not ? It looks like the total energy of an HO... BTW I'm sorry but that's the only thing I could think of
cuz in his notation (eq1.8) he has rho bar he forgot the divsion symbol. this is a book called qft in stat phys by A. Abrikosov btw. previously he mentioned in low temp He4 energy is proportional to momentum
 

dRic2

Gold Member
561
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Sorry, I'm not following. If you compare that equation with ##\frac 1 2 m \dot x ^2 + \frac 1 2 k x^2## it is straightforward to obtain ##\omega ^2 = \frac k m##
 
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ah you are right my apologies for being pretentious, your way is a pretty elegant solution
 
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Sorry, I'm not following. If you compare that equation with ##\frac 1 2 m \dot x ^2 + \frac 1 2 k x^2## it is straightforward to obtain ##\omega ^2 = \frac k m##
thank you
 

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