Browsing by Author "Wells, R. O."
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Item On Garabedian's method of solving the wave equation(1995) Oehrlein, Chris; Jones, Frank; Wells, R. O.; Anderson, JamesIn this thesis, we shall reexamine and provide as clear an exposition as possible of a method presented by P. R. Garabedian which results in an integral formula representation of a solution to the wave equation. The method involves analytically extending a harmonic function of real arguments along a purely imaginary axis in complex space and establishing the validity of the standard integral formula for harmonic functions as a representation of a solution to the Wave equation when one of the arguments is purely imaginary. This is done in the odd dimensional case by integration by parts and an application of the residue theorem, and in the even dimensional case by computing bounds on the integrals.Item On the number of bound states of the Schroedinger Hamiltonian--a review(1981) Swartz, Eric T.; Wells, R. O.; Stanton, Robert J.; Hannon, James P.We consider a non-relativistic, time independent quantum mechanical system consisting of a finite number of particles interacting via a potential, V. A sufficient condition on V that the system have an infinite number of bound states is that the particles must cluster near the continuum limit into two spatially separated clusters, and the sum of the inter-cluster two-body potentials must decay no faster than the inverse square of the inter-cluster separation. This result is proven following the work of B. Simon and W. Hunziker by showing the system reduces to a variant of the two-body problem. Many bounds for the number of bound states N(V) of the two-body system are reviewed. Most depend on integrals of V. These bounds are used to derive conditions on V so that N(V) =. If we introduce a coupling parameter, s, so that H(s)-A + sV is the two-body Hamiltonian, then we find, following the work of B. Simon [18] that N(sV) grows as s^3/2.Item The geometric relation between twistors and Minkowski space(1977) Melendez-Rojas, Oscar Roberto; Wells, R. O.The main purpose of this paper is to study some results about Twistor Theory developed by R. Penrose in a series of papers. Besides, we study geometrical relations between twistor space and complex Minkowski space in order to prove the Kerr Theorem.