Quantum detection theory
Statistical estimation theory applied to quantum mechanics and signal detection with optical instruments
Helstrom, C. W.↗
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On the rotational partition function for tetrahedral molecules
Tetrahedral molecules quantum mechanical rotational partition function, nuclear spin statistical weight factors and error bounds
Fox, K.↗
Photoelectron spectroscopy in chemistry
Polyatomic molecule photoelectron spectroscopy, emphasizing spectra interpretation by quantum mechanical procedures
Worley, S. D.↗
Sum rule functions
Sum rule functions for expressions of atomic or molecular quantum mechanical properties
Barnsley, M.↗
Noncommuting observables in quantum detection and estimation theory
In quantum detection theory, the optimum detection operators must commute; admitting simultaneous approximate measurement of noncommuting observables cannot yield a lower Bayes cost. In addition, the lower bounds on mean square errors of parameter estimates, predicted by the quantum mechanical Cramer-Rao inequality, cannot be reduced by such means.
Helstrom, C. W.↗
Noncommunting observables in quantum detection and estimation theory
In quantum detection theory the optimum detection operators must commute; admitting simultaneous approximate measurement of noncommuting observables cannot yield a lower Bayes cost. The lower bounds on mean square errors of parameter estimates predicted by the quantum-mechanical Cramer-Rao inequality can also not be reduced by such means.
Helstrom, C. W.↗
Electron impact ionization of H
The results of theoretical calculations for the reactions between electrons and negative hydrogen atoms are discussed for an electron colliding with a negative hydrogen ion and neutralizing the hydrogen ion by stripping the loosely bound electron from it, and the two free electrons moving away. A semi-quantum description of the process is presented in which the target is described in terms of quantum mechanics, and the projectile electron is described in a classical fashion.
Faisal, F. H. M.↗
Basic characteristics of high-frequency Stark-effect modulation of CO2 lasers.
The molecular Stark effect and its application to the modulation of infrared laser radiation have been investigated both theoretically and experimentally. Using a density matrix approach, a quantum mechanical description of the effect of a time-varying electric field on the absorption coefficient and refractive index of a molecular gas near an absorption line has been formulated. For modulation applications a quantity known as the ?modulation depth' is of prime importance. Theoretical expressions for the frequency dependence of the modulation depth show that the response to the frequency of a time-varying Stark field is separated into a nondispersive and a dispersive region, depending on whether the modulating frequency is less than or greater than the homogeneous absorption linewidth. Experimental results showing nondispersive modulation at frequencies to 30 MHz are presented. In addition it is shown that the response of modulation depth to Stark field amplitude is separated into linear and nonlinear regions, the field at which nonlinearities begin being determined by the absorption spectrum of the molecule being used.
Claspy, P. C.↗
Exact quantum cross sections for a three dimensional angle dependent model for three body reactions.
Exact quantum mechanical reactive cross sections are reported for a three dimensional angle dependent model surface. The surface simulates an atom-heteronuclear diatom system A + BC leading to AB + C where atom B is much heavier than A or C. The molecules BC and AB are taken to be rotating vibrators which can dissociate. Results for two angle dependent potentials are given.
Baer, M.↗
Analytic expression for the energy-transfer rate from photoelectrons to thermal-electrons.
An analytic form is given for the energy-transfer rate from photoelectrons to thermal electrons. The expression fits the classical formulation of Itakawa and Aono (1966) at low energies and gives a smooth transition to fit the quantum mechanical equation of Schunk and Hays (1971) at higher energies. The corresponding loss function or stopping power has a form that is convenient in auroral and dayglow calculations.
Swartz, W. E.↗
Energy straggling and radiation reaction for magnetic bremsstrahlung.
Using the method of quantum electrodynamics, the energy distribution of particles and emitted photons is calculated for the case when increases in the average energy of the photon emitted by synchrotron radiation to values appreciable compared to the energy of the particle give rise to particle energy straggling and radiation spectrum broadening. The classical radiative reaction effects which may be tested in this type of experiment are outlined, and a detailed quantum mechanical calculation is presented. The significance of energy straggling in astrophysics is discussed briefly.
Shen, C. S.↗
Classical laser.
In this paper a completely classical model for laser action is discussed. An active medium consisting of classical anharmonic oscillators interacts with a classical electromagnetic field in a resonant cavity. Comparison with the case of a medium consisting of harmonic oscillators shows the significance of nonlinearities for producing self-sustained oscillations in the radiation field. The results for the classical model are found to be similar to those for a semiclassical model of the ammonia-beam maser. The conclusion is that laser action is not intrinsically a quantum-mechanical effect. The classical-laser theory as given in this paper can also be applied to the case of the electron-cyclotron maser.
Borenstein, M.↗
On the relation of the infinitesimal particle propagator to the nature of mass.
From consideration of the nature of mass, in a Machian cosmological sense, it is shown that an infinitesimal particle propagator can be derived in relativistic quantum mechanics. The method used for this derivation is similar to that used in a nonrelativistic path integral.
Hoyle, F.↗
Measurement and calculation of the Stark-broadening parameters for the resonance lines of singly ionized calcium and magnesium.
The electron-impact-broadened profiles of the resonance lines of singly ionized calcium and magnesium have been measured using an electromagnetically driven shock tube and a rapid-scanning Fabry-Perot spectrometer. For an electron density of 10 to the 17th power per cu cm and a temperature of 19,000 K, we found the Lorentzian half-width of the Ca+ line to be 0.086 A plus or minus 10% and of the Mg+ line to be 0.044 A plus or minus 10%. Using the quantum-mechanical theory of Barnes and Peach and our semiclassical calculation for the calcium lines, we found that the temperature dependence of the theoretical curves is close to that measured, although both theories predict actual values which are somewhat large.
Jones, W. W.↗
Energy loss of fast electrons and positrons in a plasma.
Calculation of the stopping power of a plasma for fast electrons and positrons. First the classical limit is considered where beta = v/c is much less than alpha is the fine structure constant. Then the nonrelativistic Born-approximation formulas are derived; this domain corresponds to alpha much less than beta much less than 1. Finally, the general case of relativistic electrons and positrons is treated; in the relativistic case the scattering cross sections of Moller (electron-electron) and Bhabha (positron-electron) are used in the calculation. In all three energy domains the problem is broken up into cases of small and large momentum transfers. For large q, scattering off individual plasma electrons is considered, while in the limit of very small q for the quantum-mechanical domain, excitation of quantized plasma oscillations contributes to dE/dx; in the classical limit for small q the polarizability of the plasma provides the effective cutoff. The formulas for the stopping power differ slightly from those for a heavy ion going through a plasma because there are exchange effects and the fast electrons and positrons can lose a large fraction of their energy in one scattering off a plasma electron.
Gould, R. J.↗
On the temperature distribution in a planetary atmosphere.
Criteria for the appearance of a double maximum in the absorption spectra are derived. A very oversimplified model atmosphere which consists of two isothermal layers of gas is considered. The model involves the presence of two absorption cells in series, in front of a light source that has a higher temperature than either of the cells. The possibility that the double maximum is due to a quantum-mechanical interaction is studied. It is concluded that the effect reported by Kaplan (1962) was due to noise, and that it is impossible to detect temperatures as high as 700 K in the atmosphere of Venus by means of ground-based observations of the 7820 A carbon dioxide band.
Young, L. D. G.↗
Explicit expressions of the potential and its derivatives at the origin in terms of the scattering data
The quantum mechanical theory of scattering of a particle by a spherically symmetrical potential is presented. As in the inverse scattering problem, the input of the calculation is the scattering and bound-state data, and the output is data on the potential. The results discussed are explicit expressions for the values of the potential and its derivatives at the origin in terms of the scattering and boundstate data. Various methods to obtain these results are outlined. The presentation is aimed at introducing these various approaches. The simplest scattering problem (nonrelativistic S-wave scattering on a holomorphic potential without bound states) is used as the basis for discussion, and technicalities are omitted whenever possible without loss of clarity. A complete compilation is given of the results obtained to date in this field, including the treatment of higher partial waves and the Klein-Gordon and Dirac equations.
Calogero, F.↗
The inverse scattering problem for transmission lines
A number of exact and approximate methods for solving the inverse scattering problem for transmission lines are reviewed. In particular, the application to transmission lines of Marcenko's version of the Gelfand-Levitan exact method for the quantum mechanical problem is compared with a more direct approach based on a different version of the Gelfand-Levitan method. In addition, some aspects of the lack of uniqueness of solutions are discussed, and some open questions related to the inverse scattering problem are suggested.
Kay, I.↗