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The Energy Spectrum of the Excitations in Liquid Helium

Citation

Cohen, Michael (1956) The Energy Spectrum of the Excitations in Liquid Helium. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ATYP-VF56. https://resolver.caltech.edu/CaltechETD:etd-03192004-153651

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. 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.))
Subject Keywords:(Physics and Mathematics)
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Minor Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Feynman, Richard Phillips
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1956
Record Number:CaltechETD:etd-03192004-153651
Persistent URL:https://resolver.caltech.edu/CaltechETD:etd-03192004-153651
DOI:10.7907/ATYP-VF56
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 ETD-db
Deposited On:19 Mar 2004
Last Modified:13 Jul 2023 17:22

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