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Application of half quantum numbers to the theory of the rotational specific heat of hydrogen.—It is shown from a consideration of infra-red rotation-oscillation spectra, that the lowest possible azimuthal quantum number for a non-oscillating rotating molecule of the rigid "dumb-bell" model can have only the values zero, one, or one-half. An elementary theory of quantization in space for the new case of half quantum numbers is then developed which shows that the a priori probabilities for successive levels of rotational energy stand in the ratios of 1, 2, 3,.... The specific heat curve for diatomic hydrogen to 300°K is then calculated on the basis of the energy levels and of a priori probabilities corresponding to half quantum numbers, and is compared with the experimental points and with the curves calculated by Reiche using zero and one as the lowest possible azimuthal quantum number. At low temperatures the new curve agrees with the experimental data as well as any curve of Reiche's. At the higher temperatures, none of the curves agree with all the experimental points. The moment of inertia for the hydrogen molecule corresponding to the new curve is J=1.387×10^-41 gm cm2, about two-thirds the values assumed by Reiche, 2.095 to 2.293×10^-41, and agrees better with the conclusion of Sommerfeld from the separation of lines in the many lined spectrum of hydrogen, that the moment of inertia of an excited hydrogen molecule is 1.9×10^-41 gm cm2, which should be greater than that of the unexcited molecules involved in specific heats. Hence the possibility of half quantum numbers seems worthy of consideration.

Made available in DSpace on 2022-04-29T08:43:47Z (GMT). No. of bitstreams: 0 Previous issue date: 1969-02-01 Instituto de Física Teorica, São Paulo

There is no dearth of experimental evidence to indicate that real space-time is a four-dimensional manifold. At present there is much less certainty in attributing dimensions to the charge space of heavy particles, and it may be worth while to review various hypotheses and the meager experimental evidence in this regard. The Clebsch-Gordon coefficients for /-spin that appear in the =-N (nucleon) scattering resonance imply at least a two-dimensional space for unitary transformations (~), which are conveniently represented in the usual terms of rotations in a three-dimensional space. The apparent symmetry between E and N can be emphasized to the maximum extent by regarding the charge displacement number a = q I z of heavy particles as the third component of another vector A in charge space (~). If A is to be independent of / , there must be added an independent pair of coordinates for the unitary transformations

Following Weisskopf, the kinematics of quantum mechanics is shown to lead to a modified charge distribution for a test electron embedded in the Fermi-Dirac vacuum with interesting consequences.

A formalism is developed to deal withc-number generating functionals of quantum field theory. The general unitary relations and Schwinger equations are investigated using this formalism. Then, the formalism is used to construct a functional formulation of quantum field theory, in which state vectors are described by functionals, and field operators by functional differential operators. This formulation is in complete analogy with the wave-mechanics formulation of nonrelativistic quantum theory, in which state vectors are described by functions and observables by differential operators. Finally the case of the electromagnetic field is investigated. This framework leads to some unification of the functional formalism and simplifies the explicit calculations in many cases.

Two examples are presented: The first shows that a potentialV(x) can be in the limit circle case at ∞ even if the classical travel time to ∞ is infinite. The second shows thatV(x) can be in the limit point case at ∞ even though the classical travel time to infinity is finite. The first example illustrates the reflection of quantum waves at sharp steps. The second example illustrates the tunnel effect.

The quantum theory of diatomic dipoles.---Using the treatment of Pauli, an expression for the dielectric constant of a diatomic dipole gas is obtained, in which half-quantum numbers are used. It is shown that for cases of practical interest the approximation suggested by Pauli is not valid; hence numerical values of the temperature-function $C$ have been calculated and tabulated.Application to experimental measurements.---The theory has been applied in the interpretation of Zahn's measurements of the dielectric constants of the hydrogen halides. The electric moments of molecules of hydrogen chloride, bromide, and iodide were found to be 0.3316, 0.252, and 0.146\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}18}$ cgsu respectively; i.e., only about one-third of the values given on the basis of the classical theory. Moreover, the values 0.00077 and 0.00102 for $4\ensuremath{\pi}{N}_{0}\ensuremath{\alpha}$ for hydrogen chloride and bromide, in which $\ensuremath{\alpha}$ is the coefficient of induced polarization, are shown to be in better agreement with measurements of indices of refraction than are the classical theory values. A discussion is given of possible inaccuracies in the theory, of the choice of quantum numbers, and of the possibility of weak quantization.