Inaug.-diss.--Leipzig.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1968. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

Inaug.-diss.--Leipzig.

The derivation of a partial-wave amplitude for scattering by a separable, nonlocal potential given by MCMillan in Nuovo Cimento 29, 4153 (1963) is reviewed. Using his results, an exact expression for the amplitude is derived for a potential of the form -g V(r)V(r¹), where V(r) = ra e-μr , and its analytic properties are studied. The asymptotic behaviour of the amplitude as |ℓ| → ∞ (where ℓ is the usual angular-momentum parameter) is derived, and is shown to permit a Sommerfeld-Watson transformation to be performed on the series expression for the total scattering amplitude in terms of the partial-wave amplitudes. By means of this transformation, a double-dispersion relation is derived for the total amplitude in both the complex-energy and complex-cos θ planes. Explicit forms are derived for the weight functions, and the convergence of the integrals involved is studied. In addition to the usual branch cuts along the positive, real energy and cos θ axes, an extra cut along the negative , real energy axis is found which is not present for the local case. Its origin is traced to the fact that the Wronskian of two solutions of the nonlocal radical Schroedinger equation is not necessarily a constant, as it is in the purely local case; and to the conditions necessary to ensure convergence of the extra integral in the nonlocal Schroedinger equation. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

On presente une generalisation d'un resultat de Wallin ainsi qu'une caracterisation des ensembles compacts polaires dans un espace de Brelot. Ces resultats se generalisent a un produit de n espaces de Brelot en demontrant la continuite des fonctions multireduites. On en deduit qu'un ensemble localement n polaire est un ensemble in polaire. Des resultats semblebles ont lieu pour une sous-classe des ensembles pluripolaires dans un domaine hyperconvexe et borne de C('n).

Thesis (M.S.)--Ohio University, June, 1999. / Title from PDF t.p.

In studying the diamagnetism of free electrons in a uniform magnetic field it was found that reducing the field to zero in the wavefunction did not yield the experimentally indicated free particle plane wave wavefunction. However, solving the Schroedinger Equation resulting from setting the field equal to zero in the original equation did yield a plane wave wavefunction. This paradox was not found to be peculiar to the case of a charged particle in a uniform magnetic field but was found to occur in a number of other systems. In order to gain an understanding of this unexpected behavior, the following systems were analyzed: the one-dimensional square well potential; a charged, spinless particle in a Coulomb field and in a uniform electric field; a one-dimensional harmonic oscillator; and a charged, spinless particle in a uniform magnetic field. From these studies the following were obtained: conditions for determining the result of reducing the potential in a wavefunction; the condition under which the potential of a system may be switched off while maintaining the energy of the system constant; the relationship between the result of physically switching off a potential, the result of reducing it in the wavefunction, and the solution of the Schroedinger Equation obtained by decreasing the potential to zero in the original wave equation; and a general property of any wavefunction with respect to reducing any parameter within this wavefunction. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

No description available.

Thesis (doctoral)--Uppsala universitet, 1917. / Includes bibliographical references.

No description available.