A systematic procedure is developed for solving the eigenvalue problem for a broad class of Hamiltonian operators containing no terms higher than quadratic in generalized coordinates and th e ir conjugate momenta. The development is oriented toward practica l applications in the area o f the many-body problem. The procedure accomplishes a canonical reduction of such a Hamiltonian to the form of the Hamiltonian fo r a co llec tion of non in teracting bosons, with the eigenvalues of the Hamiltonian expressed in terms of the solutions to a single secular equation. Application of the resu lts to systems o f in teracting identical bosons is discussed, including a presentation of a useful calcu latlonal technique. The procedures developed are i l lu s tra te d by deta iled treatments o f two specific problems o f in terest in physics. The f i r s t problem considered is an exactly solvable separable potentia l model of p a r t ic le f ie ld theory. This problem consists of the description o f a co llec tio n of l ig h t bosons in teracting with an in f in i t e ly heavy boson v ia a simple separable p o te n tia l . In te res t in th is problem centers on i ts use as a test case for approximation techniques to be used on more complicated systems. The second and more r e a l is t ic problem investigated is the polaron problem of solid s ta te physics. This problem involves the

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James Lannis Roberts

Papers

a Systematic Study and Applications of the Eigenvalue Problem for Quadratic Hamiltonians.