Thesis (Ph. D.)--University of Washington, 2007. / Vita. Includes bibliographical references (leaves 268-273).

Proefschrift Universiteit Leiden. / Description based on print version record. Includes bibliographical references and index.

Thesis (M.S.) -- Worcester Polytechnic Institute. / Keywords: Mori ; Projected dynamics. Includes bibliographical references (leaves 48-49).

No description available.

The aim of this work is to propose a possible explanation of certain conservation laws which hold in the reactions among elementary particles. The laws in question are those of conservation of baryon number and conservation of lepton numbers. These are additive quantum numbers which take the values +1, -1, or 0, for single particles. At the present time, these laws must be considered as empirical conservation laws, whose origin is not known. Certain universal symmetry operations must be represented by anti-unitary operators whose square is -1. The existence of such an operator leads to a super-selection rule. The Hilbert space is decomposed into two orthogonal subspaces, with no observables having matrix elements connecting the two subspaces. In the presence of a super-selection rule, an operator can be constructed, which is an observable whose eigenvalues are conserved, and whose eigenvalues have the properties of an additive quantum number. One has one such operator for the baryons, and two for the leptons. A consistent classification of the elementary particles is worked out, which allows the conservation laws to be explained as a result of super-selection rules, provided that the masses of the particles have suitable transformation properties. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The object of the work reported in this thesis was to construct and study the explicit representations of discrete symmetry operators (D.S.O.'s) in quantum field theory. In spite of the considerable importance of the D.S.O.'s in present day physics, not much has been reported in the systematic study of such representations. Furthermore, in the work reported hitherto, only incomplete representations for the operators of space inversion (⊓) particle conjugation (⌐) and time reversal ( T ) have been given. Starting from general considerations on invariance principles and infinitesimal transformations, with the associated conservation laws, a systematic procedure for constructing the representations of the D.S.O.'s has been formulated. The procedure consists in enumerating the bilinears in creation and annihilation operators. It is shown that eight symmetries are the only possible ones. In view of the TCP - theorem and the so called non-conservation of parity in weak interactions, the product operators, such as reflection ( ⋀ = ⊓ ⌐ ) and strong reflection (S = ⊓ ⌐ T), in addition to time reversal, should be considered as the most basic symmetries. Working in linear momentum representation, the unitary operators ⋀, ⊓, ⌐, E ( = identity) and the unitary factors of the antiunitary operators: S, I = ⊓ T, J = T ⌐ and T are constructed for the following free fields: (I) The non-hermitian scalar field representing, for example, kaons. (II) The electromagnetic field. (III) The four-component spinor field. The operators for the scalar field have also been worked out in the angular momentum representation. Using the anti-commutation relations for C.O.’s and A.O.’s, an alternate construction of D.S.O.'s of the Dirac field is exhibited. More than one representation has been given in each case. In addition a two dimensional matrix representation has been given. It is shown that by an appropriate unitary transformation these can be reduced to the ordinary form. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The solutions of the radial part of the Schrödinger equation for the hydrogen atom, which may be written (in atomic units) as [-1/r² d/dr r² d/dr + ℓ(ℓ + 1)/ r² - 2/r] Ψ(r) = EΨ(r) are well known in the standard case when the boundary conditions require that the wave function should vanish for infinite r . The eigenfunctions in this case are expressible in terms of Laguerre polynomials and the eigenvalues of the energy are E[subscript n] = - 1/n² ( n = 1, 2 ...) The problem of determining the eigenvalues when the boundary conditions require that Ψ should vanish for a finite r , say r₀ , is not as amenable to solution, and it is only recently that several methods have been suggested for dealing with this case. The method to be discussed here is due to Michels, de Boer, and Bijl. De Boer, considering the ground state alone, succeeds through the use of a perturbation method in finding the change in the eigenvalues for different r₀ . In so doing, he makes an approximation, which a priori is not justified. In the present thesis, it is shown both qualitatively and quantitatively that the approximation is justified for the values of r₀ used. The logical extension of the method to states other than the ground state is made for two particular cases, and from the results of these two investigations, conclusions are drawn regarding the general applicability of de Boer's method. / Science, Faculty of / Mathematics, Department of / Graduate

The problem of a particle in two adjacent one-dimensional rectangular, potential "boxes" is an exactly soluble representative of a class of two-minima problems of considerable physical interest which have not been solved exactly. It therefore affords a valuable opportunity for a critical examination of the extent of applicability of perturbation theory methods to such problems. An exact implicit solution of the problem is obtained, and is reduced to explicit approximate form in two important special cases. These approximations are reproduced by perturbation theory methods, and their ranges of validity are demonstrated by comparison with the exact solution. The application of the model to a physical system is demonstrated by using the identical two-box problem as a basis for calculation of some constants of the ammonia molecule. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The variation with temperature of electron tunneling through thin insulating films of A1₂0₃ between aluminum film electrodes was studied at liquid helium temperatures (1.18°K to 4.2°K) and liquid oxygen temperatures (65°K to 90°K). Samples were prepared in a vacuum evaporating system using the method developed by Fisher and Giaever (1961). The aluminum oxide films were grown in air at room temperature. Resistance was measured as a function of voltage by means of a d.c. Wheatstone bridge for sample currents in the region of 10⁻⁷ amps. Conduction due to electron tunneling was indicated by the non-ohmic voltage dependence of resistance and by the fact that the resistance increased with a decrease in temperature. The voltage dependence of the tunneling resistance was found to be in good agreement with the theory as derived by Simmons (1963), and was parabolic for low voltages. Reliable and reproducible data for the temperature dependence of resistance were difficult to obtain because of instabilities in the samples and a general increase in resistance due to aging. Comparison of the observed temperature dependence with the theory of Simmons (1964) showed the variation to be approximately twice as great as predicted. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The thesis investigates the possibility of a classical semantics for quantum propositional structures. A classical semantics is defined as a set of mappings each of which is (i) bivalent, i.e., the value 1 (true) or 0 (false) is assigned to each proposition, and (ii) truth-functional, i.e., the logical operations are preserved. In addition, this set must be "full", i.e., any pair of distinct propositions is assigned different values by some mapping in the set. When the propositions make assertions about the properties of classical or of quantum systems, the mappings should also be (iii) "state-induced", i.e., values assigned by the semantics should accord with values assigned by classical or by quantum mechanics. In classical propositional logic, (equivalence classes of) propositions form a Boolean algebra, and each semantic mapping assigns the value 1 to the members of a certain subset of the algebra, namely, an ultrafilter, and assigns 0 to the members of the dual ultraideal, where the union of these two subsets is the entire algebra. The propositional structures of classical mechanics are likewise Boolean algebras, so one can straightforwardly provide a classical semantics, which also satisfies (iii). However, quantum propositional structures are non-Boolean, so it is an open question whether a semantics satisfying (i), (ii) and (iii) can be provided. Von Neumann first proposed (1932) that the algebraic structures of the subspaces (or projectors) of Hilbert space be regarded as the pro-positional structures PQM of quantum mechanics. These structures have been formalized in two ways: as orthomodular lattices which have the binary operations "and", "or", defined among all elements, compatible [symbol omitted] and incompatible [symbol omitted]; and as partial-Boolean algebras which have the binary operations defined among only compatible elements. In the thesis, two basic senses in which these structures are non-Boolean are discriminated. And two notions of truth-functionality are distinguished: truth-functionality [symbols omitted] applicable to the PQM lattices; and truth-functionality [symbol omitted] applicable to both the lattices and partial-Boolean algebras. Then it is shown how the lattice definitions of "and", "or", among incompatibles rule out a bivalent, truth-functional [symbols omitted] semantics for any lattice containing incompatible, elements. In contrast, the Gleason and Kochen-Specker proofs of the impossibility of hidden-variables for quantum mechanics show the impossibility of a bivalent, truth-functional [symbol omitted] semantics for three-or-higher dimensional Hilbert space structures; and the presence of incompatible elements is necessary but is not sufficient to rule out such a semantics. As for (iii), each quantum state-induced expectation-function on a PQM truth-functionally assigns 1 and 0 values to the elements in a ultrafilter and dual ultraideal of PQM³ where, in general the union of an ultrafilter and its dual ultraideal is smaller than the entire structure. Thus it is argued that each expectation-function is the quantum analog of a classical semantic mapping, even though the domain where each expectation-function is bivalent and truth-functional is usually a non-Boolean substructure of PQM. The final portion of the thesis surveys proposals for the introduction of hidden variables into quantum mechanics, proofs of the impossibility of such hidden-variable proposals, and criticisms of these impossibility proofs. And arguments in favour of the partial-Boolean algebra, rather than the orthomodular lattice, formalization of the quantum propositional structures are reviewed. / Arts, Faculty of / Philosophy, Department of / Graduate