Citation
Cohen, Michael (1956) The energy spectrum of the excitations in liquid helium. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd03192004153651
Abstract
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Feynman has used the wave function [...] to represent an excitation (phonon or roton) of momentum [...] in liquid helium. [...] is the ground state wave function, and the sum runs over all the atoms in the liquid. The resultant energy spectrum is correct for phonons [...] and has the qualitatively correct feature of exhibiting a minimum at [...] (roton region). Landau and subsequent workers have shown that the specific heat and second sound velocity data require the value [...], where [...] is the minimum roton energy and [...] is Boltzmann's constant. Feynman's energy spectrum locates the minimum correctly but gives [...].
A wave function of the form [...] is proposed here to represent an excitation of momentum [...]. The function g represents the fact that the neighbors of a moving atom execute some smooth pattern of backflow around it; g is taken as the potential function for a dipole velocity field, the strength of the dipole being left arbitrary until the end of the computation. To facilitate computation, it proves useful to replace [...]. This procedure is mathematically legitimate, not only because [...] is small, but because the wave function is inserted into a variational principle for the energy and is guaranteed to yield an overestimate. The strength of the dipole is finally chosen to minimize the energy yielding the new value [...]. The optimal value for the dipole strength is very close to the "classical" value which one would expect on the basis of a current conservation argument.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Physics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  1 January 1956 
Record Number:  CaltechETD:etd03192004153651 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd03192004153651 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  1007 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  19 Mar 2004 
Last Modified:  26 Dec 2012 02:34 
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