Reuben Benumof

Optical Pumping Theory and Experiments

The theory of several experiments involving optical pumping is presented in a simplified form. Vector methods are employed to discuss the hyperfine energy levels of an atom in a weak magnetic field, and, for the purposes of considering relaxation time, the system is assumed to have only two effective levels. The Breit-Rabi equation for the ground-state hyperfine Zeeman energy levels of an alkali atom is derived from the Schrodinger equation to facilitate the interpretation of the quadratic Zeeman effect. A number of suggestions for practical optical pumping experiments are made.

Momentum propagation by traveling waves on a string

The one‐dimensional wave equation for traveling transverse waves on a string implies three interesting consequences. (1) A traveling wave propagates both transverse and longitudinal momentum. (2) The time‐rate of change of longitudinal momentum density is equal to the space‐rate of decrease of stored energy density. (3) The longitudinal momentum density wave travels with the same speed as the displacement wave but may have a different form. As a result of the transmission of longitudinal momentum, longitudinal forces are exerted on both absorbers and reflectors.

The receiving antenna

The basic theory of a receiving antenna is presented in sufficient detail to permit the calculation of the voltage across the load of an optimally designed TV antenna circuit. The rms load voltage is given by VL=λH(30RrD)1/2, where λ is the wavelength of the incident radiation, H is the rms value of the magnetic field intensity, Rr is the radiation resistance of the antenna, and D is the directive gain. The result obtained from this formula for a typical monopole TV antenna is compared with that obtained from a simple, intuitive approximation. The reasons for the difference in the results are discussed.

Simple harmonic motion in harmonic plane waves

The displacement of a particle in a medium in which there is a traveling or standing harmonic plane wave is a sinusoidal function of the time, and the particle may therefore be said to execute simple harmonic motion. An incorrect view of this motion is that it is identical to the free vibration of a mass attached to a massless spring. In general, the total energy of a particle in the medium varies from zero to a maximum. In the case of standing waves, the energy surges from the nodes, where it is entirely potential, to the antinodes, where it is entirely kinetic, and back again. The paradox of a transverse traveling wave on a string transmitting longitudinal momentum is resolved by noting that a differential length of string stretches as its slope increases. A point on the string has a small longitudinal motion in addition to its transverse motion.

Simple astronomical theory of climate

By applying perturbation theory to a highly simplified solar system, we find that the semimajor axis of the Earth’s orbit is secularly invariant, the square of the eccentricity varies approximately sinusoidally with a secular period of 93 000 years, and the perihelion precesses toward the northern summer solstice with a period of approximately 21 000 years relative to the moving vernal equinox. The Earth’s axis also nutates with a period of 41 000 years. These periods correlate very well with the periods found in the climatic record. The secular periods of the Earth’s orbital parameters determine the variation with time of the average intensity of solar radiation and thus may trigger the onset of ice ages.

Astronomical meaning of a tropical year

A tropical year is usually described incorrectly as the actual interval between two successive passages of the Sun through the vernal equinox. These intervals vary from year to year because of the differing periods of the perturbations of the angular velocity of the Earth. A tropical year is correctly defined as the mean interval between two successive passages of the Sun through the mean equinox of date. The time of beginning of spring depends on (i) the perturbations of the angular velocity of the Earth, (ii) the nutation of the Earth’s axis, and (iii) the aberration of light.

The Energy and Momentum of a Classical Electron in Special Relativity

An equation for the energy of a “classical” electron is derived from Maxwells equations. The reason for carefully specifying the time at which certain integrations are performed is established. The momentum of the electron is treated in a similar manner. The results are in complete agreement with the special theory of relativity.