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The energy spectrum of the excitations in liquid helium


Cohen, Michael (1956) The energy spectrum of the excitations in liquid helium. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ATYP-VF56.


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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):
  • Feynman, Richard Phillips
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1956
Record Number:CaltechETD:etd-03192004-153651
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1007
Deposited By: Imported from ETD-db
Deposited On:19 Mar 2004
Last Modified:21 Dec 2019 04:26

Thesis Files

PDF (Cohen_m_1956.pdf) - Final Version
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