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    An investigation of a class of soluble many body problems

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    Author
    Edwards, Gregg Stanley
    Date
    1963
    Advisor
    Trammell, George T.
    Degree
    Master of Arts
    Abstract
    This thesis is a report of results so far obtained in an investigation of the properties and characteristics of simple interaction systems whose Hamiltonians are quadratic in their generalized coordinates. The exact solutions of two system types are presented. The first is composed of a simple harmonic oscillator coupled to a uniform lattice of coupled simple harmonic oscillators, or, in the small amplitude approximation, to a beaded string. The second is composed of an arbitrary distribution of oscillators coupled to string. The quantization of linear systems such as those described above is discussed with the result that the solution to the equivalent quantum system in terms of operators is just that of the corresponding classical solution as a function of its initial conditions when these are interpreted as quantum operators. The energy flow along the linear chain is examined in the discussion of the non-exponential decay in dispersive systems. This is compared with the original discussion by Trammell (1956) who pointed out the non-exponential decay of quantum systems and the corresponding behavior of dispersive classical systems.
    Citation
    Edwards, Gregg Stanley. "An investigation of a class of soluble many body problems." (1963) Master’s Thesis, Rice University. https://hdl.handle.net/1911/89837.
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    Managed by the Digital Scholarship Services at Fondren Library, Rice University
    Physical Address: 6100 Main Street, Houston, Texas 77005
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    Site Map