Volume 82, Issue 8, August 2014

In the coherent state of the harmonic oscillator, the probability density is that of the ground state subjected to an oscillation along a classical trajectory. Senitzky and others pointed out that there are states of the harmonic oscillator corresponding to an identical oscillatory displacement of the probability density of any energy eigenstate. These generalizations of the coherent state are rarely discussed, yet they furnish an interesting set of quantum states of light that combine features of number states and coherent states. Here, we give an elementary account of the quantum optics of generalized coherent states.
 PAPERS


Generalized coherent states
View Description Hide DescriptionIn the coherent state of the harmonic oscillator, the probability density is that of the ground state subjected to an oscillation along a classical trajectory. Senitzky and others pointed out that there are states of the harmonic oscillator corresponding to an identical oscillatory displacement of the probability density of any energy eigenstate. These generalizations of the coherent state are rarely discussed, yet they furnish an interesting set of quantum states of light that combine features of number states and coherent states. Here, we give an elementary account of the quantum optics of generalized coherent states.

An introduction to QBism with an application to the locality of quantum mechanics
View Description Hide DescriptionWe give an introduction to the QBist interpretation of quantum mechanics, which removes the paradoxes, conundra, and pseudoproblems that have plagued quantum foundations for the past nine decades. As an example, we show in detail how this interpretation eliminates “quantum nonlocality.”

The fields of a charged particle in hyperbolic motion
View Description Hide DescriptionA particle in hyperbolic motion produces electric fields that appear to terminate in midair, violating Gauss's law. The resolution to this paradox has been known for sixty years but exactly why the naive approach fails is not so clear.

Trajectory of a projectile on a frictional inclined plane
View Description Hide DescriptionA closed form solution is given for the trajectory of a particle sliding on an inclined plane with Coulombtype friction. If the inclination of the plane is less than the friction angle, the particle eventually comes to rest and expressions for the location of this point and the duration of the motion are given. If the initial launch is inclined at a small angle with respect to the upward line of greatest slope, the direction of the velocity changes rapidly during the last instants of motion.

Why do Earth satellites stay up?
View Description Hide DescriptionSatellites in low Earth orbits must accurately conserve their orbital eccentricity, since a decrease in perigee of only 5–10% would cause them to crash. However, these satellites are subject to gravitational perturbations from Earth's multipole moments, the Moon, and the Sun that are not spherically symmetric and hence do not conserve angular momentum, especially over the tens of thousands of orbits made by a typical satellite. Why then do satellites not crash? We describe a vectorbased analysis of the longterm behavior of satellite orbits and apply this to several toy systems containing a single nonKeplerian perturbing potential. If only the quadrupole (or J 2) potential from the Earth's equatorial bulge is present, all nearcircular orbits are stable. If only the octupole (or J 3) potential is present, all such orbits crash. If only the lunar or solar potential is present, all nearcircular orbits with inclinations to the ecliptic exceeding are unstable. We describe the behavior of satellites in the simultaneous presence of all of these perturbations and show that almost all low Earth orbits are stable because of an accidental property of the dominant quadrupole potential. We also relate these results to the phenomenon of Lidov–Kozai oscillations.

Measuring Gaussian noise using a lockin amplifier
View Description Hide DescriptionGaussian fluctuations (or Gaussian noise) appear in almost all measurements in physics. Here, a concise and selfcontained introduction to thermal Gaussian noise is presented. Our analysis in the frequency domain centers on thermal fluctuations of the position of a particle bound in a onedimensional harmonic potential, which in this case is a microcantilever immersed in a bath of roomtemperature gas. Position fluctuations of the microcantilever, detected by the optical beam deflection technique, are then fed into a lockin amplifier to measure the probability distribution and spectral properties of the fluctuations. The lockin amplifier measurement is designed to emphasize the frequencydomain properties of Gaussian noise. The discussion here can be complementary to a discussion of Gaussian fluctuations in the time domain.

Response of a lockin amplifier to noise
View Description Hide DescriptionThe “lockin” detection technique can extract, from a possibly noisy waveform, the amplitude of a signal that is synchronous with a known reference signal. This paper examines the effects of input noise on the output of a lockin amplifier. We present quantitative predictions for the rootmeansquare size of the resulting fluctuations and for the spectral density of the noise at the output of a lockin amplifier. Our results show how a lockin amplifier can be used to measure the spectral density of noise in the case of a noiseonly input signal. Some implications of the theory, familiar and surprising, are tested against experimental data.
