A Caltech Library Service

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.


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:
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:13 Jul 2023 17:22

Thesis Files

PDF (Cohen_m_1956.pdf) - Final Version
See Usage Policy.


Repository Staff Only: item control page