Showing papers on "Semiclassical physics published in 1969"
TL;DR: In this paper, the authors derive "classical" equations for the relative motion of two atoms as their insides make a given quantum transition, based on a generalization of Hamilton's principle, suggested by Feynman's formulation of quantum mechanics.
Abstract: We derive "classical" equations for the relative motion of two atoms as their insides make a given quantum transition. The classical changes in relative energy and angular momentum associated with this description just balance the corresponding quantum changes in internal energy and angular momentum for the transition involved. The work is based on a generalization of Hamilton's principle, suggested in a natural way by Feynman's formulation of quantum mechanics; the semiclassical scattering theory which emerges is, in essence, a justification and extension of the impact-parameter method. Applications to low-energy atomic collisions are discussed briefly.
310 citations
TL;DR: In this paper, the authors derived the semiclassical theory of potential scattering from Feynman's path-integral formulation of quantum mechanics and applied it to scattering by a noncentral field.
Abstract: The semiclassical theory of potential scattering is derived from Feynman's path-integral formulation of quantum mechanics. Since the partial-wave expansion is avoided, the results are applicable to scattering by a noncentral field. Special attention is given to the conditions for validity of the semiclassical approximation.
279 citations
TL;DR: In this paper, a classical theory of stimulated Raman scattering is constructed, which is an extension of the theory of Shen and Bloembergen, and the conditions for the transient and steady-state gains are discussed.
Abstract: The semiclassical theory of spontaneous Raman scattering is reviewed. From the semiclassical theory we identify the parameters and dynamical variables involved in Raman scattering. A classical theory of stimulated Raman scattering is constructed. It is an extension of the theory of Shen and Bloembergen. We show that the system is a weakly coupled system. Because the driving term contains dynamical variables, the linewidth of the stimulated Stokes wave should be smaller than that of the spontaneous Stokes wave. Using Riemann's method, we obtain Kroll's solution rigorously, in a more general form. The steady-state limit is also derived rigorously. The conditions for the transient and steady-state gains are discussed. It is shown that for the transient case one may have an abrupt change of the Stokes gain versus incident laser power.
151 citations
TL;DR: Lamb theory of Doppler broadened gas laser extended to arbitrary intensities for single mode operation, calculating detuning curves and inversion densities as mentioned in this paper, for single-mode operation.
Abstract: Lamb theory of Doppler broadened gas laser extended to arbitrary intensities for single mode operation, calculating detuning curves and inversion densities
118 citations
TL;DR: Semiclassical approximations for the angular dependence of the scattering cross section σ(θ) for two cases, involving the forward and backward directions, where the classical scattering is infinite, were derived in this article.
Abstract: Semiclassical approximations are derived for the angular dependence of the scattering cross section σ(θ) for two cases, involving the forward and backward directions, where the classical scattering is infinite. The results are approximations uniform in angle and valid from the ordinary semiclassical region where σ(θ) is O(0) right round to θ = 0 or π for a glory σ(θ) is then O(-1) and the forward diffraction peak σ(θ) is O(-2) or larger, depending on the form of the long-range tail of the scattering potential. The formulae are all expressed in terms of the action functions along the paths of the classical problems.
62 citations
TL;DR: In this paper, the authors extended quantum field calculations to include atomic field effect on atom, predicting spontaneous decay rate from excited state and light frequency time dependence, and extended the quantum field calculation with atomic field effects on atom.
Abstract: Unquantized field calculations extended to include atomic field effect on atom, predicting spontaneous decay rate from excited state and light frequency time dependence
47 citations
TL;DR: In this article, the WKB method was used to solve a set of coupled radial differential equations for an exact quantal calculation of multiple Coulomb excitation, which can be used to facilitate the computations.
46 citations
TL;DR: In this paper, a hierarchy of related semiclassical approximations for treating molecular inelastic scattering is derived, starting from the coupled Schrodinger equations of motion, the radial wavefunctions are expressed as ui(r)
Abstract: A hierarchy of related semiclassical approximations is derived for treating molecular inelastic scattering. Starting from the coupled Schrodinger equations of motion, the radial wavefunctions are expressed as ui(r) = u1i(r)Xi(r) + u2i(r)Yi(r), where u2i and u2i are two linearly independent approximate solutions for elastic scattering. A set of coupled first‐order equations for Xi and Yi is obtained. By using simple WKB wavefunctions for u1 and u2 and by neglecting several terms, the coupled time‐dependent equations and several previous semiclassical approximations can be readily obtained. Inclusion of the neglected terms yields improved accuracy for these approximations. Use of modified WKB wavefunctions valid near the classical turning point extends these approximations to cases involving large energy transfer where the inelastic cross sections are sensitive to the region near the turning point. In the sudden and “classical” limits of the internal molecular motions the coupled equations in X and Y can be...
37 citations
TL;DR: In this article, a quantization formula for the energy levels of an asymmetric double well oscillator was derived using the phase integral approach, and the connection with phase integral approaches to this problem was discussed.
36 citations
TL;DR: In this paper, a comparison between the semiclassical and quantum-mechanical treatment of the anomalous skin effect is made, and the value of the surface impedance with both theories is calculated.
Abstract: A comparison is made between the semiclassical and the quantum-mechanical treatment of the anomalous skin effect. The latter theory is based on the density matrix. The author calculates the value of the surface impedance with both theories. The difference depends on a parameter $\ensuremath{\lambda}$, which is the ratio of the skin depth to a typical de Broglie wavelength. This wavelength corresponds to the velocity component, normal to the surface, of an effective electron. The order of magnitude of the correction depends on the relaxation time, and can amount to 10% for sufficiently pure metals.
TL;DR: In this paper, explicit expressions for the semiclassical transition probabilities of atomic $K$- and $L$-shell electrons into the continuum as a result of proton collisions are obtained as functions of the proton impact parameter and energy transfer, using first-order time-dependent perturbation theory with undeflected proton trajectories.
Abstract: Explicit expressions for the semiclassical transition probabilities of atomic $K$- and $L$-shell electrons into the continuum as a result of proton collisions are obtained as functions of proton-impact parameter and energy transfer, using first-order time-dependent perturbation theory with undeflected proton trajectories. Calculated energy distributions for the ejected electrons are compared with the plane-wave Born-approximation cross sections. The contributions from various partial waves are shown in illustrations. The validity of the calculation is limited by the neglect of the Coulomb deflection of the protons.
TL;DR: In this article, the cluster integral of second order for quantum plasmas was given by a definite integral over the SLATER sum of two particles, which was calculated exactly, using the method of perturbation theory with respect to the interaction parameter e2 for the orders e2k with k ≦ 3.
Abstract: In part I of this paper the cluster integral of second order for quantum plasmas was given by a definite integral over the SLATER sum of two particles. Here this integral is calculated exactly, using the method of perturbation theory with respect to the interaction parameter e2 for the orders e2k with k ≦ 3, and the method of scattering phase shifts for the orders e2k with k ≧ 4. The cluster integral of second order is expressed by quantum virial functions and exchange virial functions. These functions are expressed in form of integrals over the complex energy plane. From these integrals TAYLOR expansions and asymptotic representations of the virial functions are derived. In the case of lower temperatures, the semiclassical formulae derived by LARKIN and the author are obtained, using the first terms of the asymptotic representation.
01 Jan 1969
13 Feb 1969-Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences
TL;DR: In this article, the authors describe the operation of a laser by a method patterned closely after the classical theory of dispersion, where the electromagnetic field is treated as a classical system interacting with a collection of classical harmonic oscillators which are at rest.
Abstract: This present paper is an attempt to describe the operation of a laser by a method patterned closely after the classical theory of dispersion. There, the electromagnetic field is treated as a classical system interacting with a collection of classical harmonic oscillators which are at rest. In the present case the radiation field is still treated classically, but, in accordance with the correspondence principle, the oscillators are now virtual oscillators associated with the up-and-down transitions in effective two-state atoms which are described quantum mechanically. The atoms carrying these virtual oscillators are not at rest but move with different velocities. We show how the Lorentz averaging can be performed for such systems, and derive a closed set of equations linking the average electric field E, with the average polarization density P„ and the average population inversion density Mp associated with atoms moving with the velocity v. Next, we investigate the conditions for the existence of a steady state if pumping is present, and if the electric field is represented by a standing wave, or a travelling wave of a single frequency (single-mode case). It turns out that, notwithstanding the nonlinear nature of the equations, the steady-state conditions give a simple complex dispersion relation; moreover, the real and imaginary part of this dispersion relation are equivalent to the usual heuristic expressions which specify the operating frequency in terms of the index of refraction and cavity length, and which balance the gain against the losses. The single-mode case is analysed in detail without any smallness assumptions for the resultant intensity. The small-intensity case gives the usual results exhibiting the tuning dip. For high intensities the relative depth of the dip tends to zero. At the end of the paper we discuss proposed extensions and additional applications.
TL;DR: In this article, the quantum theory of the laser is compared to the semiclassical theory for stationary atoms, and the spatial structure of the cavity mode is found to be important, taking into account this structure full agreement between quantum and SFA results.
TL;DR: Stueckelberg formulation for transition probabilities to interpret perturbation effects in elastic scattering differential cross section measurements was used in this paper, where the Stueckeberg formulation was applied to elastic scattering cross-section measurements.
Abstract: Stueckelberg formulation for transition probabilities to interpret perturbation effects in elastic scattering differential cross section measurements
TL;DR: In this article, the exact diamagnetic susceptibility is calculated as a function of the magnetic field for a magnetic breakdown model which has been previously presented, and the susceptibility is obtained by numerically evaluating the appropriate derivative of the Helmholtz free energy using the exact eigenvalues of the model Hamiltonian.
TL;DR: In this paper, the distorted wave Born approximation (DWBA) with a semiclassical (WKB) description of relative translational motion is used to characterize final-state interactions in the collision of an atom with a diatomic molecule.
Abstract: The distorted‐wave Born approximation (DWBA) with a semiclassical (WKB) description of relative translational motion is used to characterize final‐state interactions in the collision of an atom with a diatomic molecule. The resulting cross section is found to be the product of one factor that varies slowly with energy and another which characterizes the final‐state interaction. This latter factor, containing the resonant‐type of energy dependence, is determined solely by the distorting potential, being independent of the interaction producing the given transition. Simple physical interpretations and useful extensions are obtained by employing the concept of time delay.
01 Jan 1969
TL;DR: In this article, the first few moments of the number of photoelectrons ejected in time internal [0, T] were obtained by taking the correlations in intensity of the photon beam at different times.
Abstract: It was the thesis of Toynbee that great religions arise by the encounter of two great civilizations. The Graeco-Roman civilization meeting the Syrian civilization is supposed to have produced Christianity. Be that as it may, we know for certain that meeting of two disciplines of thought or even two subdisciplines in the same categories produce fascinating results. One such very fruitful encounter is the application of stochastic theory of point processes to the theory of interference in light beams. A new element was injected into this field, by the wellknown Brown and Twiss experiment1 which opened up a new chapter on “photon statistics and coherence” in optics. A semiclassical study of these coherence properties and the statistics of the ejected electrons has been carried out by Glauber, Sudarshan, and others2 using P- representations or quasi-probability distributions. These are density matrix descriptions obtained by a knowledge of the coherent state formulation of the photon fields. Mandel3 adopted a simpler procedure of obtaining the first few moments of the number of photoelectrons ejected in time internal [0, T], by taking the correlations in intensity of the photon beam at different times. They all found that the first few moments coincided with those of the Bose distribution for the number of photolectrons emitted by thermal light. However, a general method can be adopted to find the probability distribution of photoelectrons if one knows all orders of correlations in intensity existing in the incident beam.
TL;DR: In this paper, the N-state semiclassical approach was used in the calculation of vibrational transition probabilities for atom-Morse-oscillator collinear collisions.
Abstract: The N‐state semiclassical approach is used in the calculation of vibrational transition probabilities for atom–Morse‐oscillator collinear collisions. Exact semiclassical calculations for several initial classical phases are compared with rigid‐body results. The transition probabilities are found to be strongly dependent upon the initial phase. Two procedures are used for matching the Morse potential to a quadratic potential. The resulting transition probabilities indicate that the potentials should be matched on their repulsive sides rather than at their minima.
01 Jan 1969
TL;DR: Semiclassical approximations for the angular dependence of the scattering cross section a(@) were derived for two cases, involving the forward and backward directions, where the classical scattering is infinite as discussed by the authors.
Abstract: Semiclassical approximations are derived for the angular dependence of the scattering cross section a(@ for two cases, involving the forward and backward directions, where the classical scattering is infinite. The results are approximations uniform in angle and valid from the ordinary semiclassical region where a@) is O(fio) right round to 0 = 0 or v; for a glory a(@ is then O(Vl-l) and the forward diffraction peak a(@ is O(Vl-2) or larger, depending on the form of the long-range tail of the scattering potential. The formulae are all expressed in terms of the action functions along the paths of the classical problems.
TL;DR: In this paper, the authors studied the response of a laser system to a monochromatic electromagnetic standing wave through joint solution of Maxwell's equations and the equations for the density matrix.
Abstract: The kinetic equation for the density matrix is used to study the response of a laser system to a monochromatic electromagnetic standing wave. Steady-state laser operation is studied through joint solution of Maxwell's equations and the equations for the density matrix. Allowances are made for nonuniformities in the radiating medium modulated by the field and for the motion of the radiating particles. Steady-state operating conditions and oscillation thresholds for gas and solid-state lasers are compared.
TL;DR: In this paper, the cross section and polarization of nucleons elastically scattered at large angles were obtained from the optical model assumptions using a semiclassical approximation, and the formulae thus obtained agree well with experimental data.
TL;DR: In this paper, the mutual influence of two laser modes corresponding to two different transitions with the same lower level was investigated experimentally in a HeNe-d.c.-laser.
Abstract: The mutual influence of two laser modes corresponding to two different transitions with the same lower level is investigated experimentally in a HeNe-d.c.-laser for the laser transitions 2s2 → 2p4 and 3s2 → 2p4. The results are in agreement with calculations in the frame of semiclassical theory of laser action [2].
TL;DR: In this paper, the symmetry and boundary conditions of quantum statistical correlation functions of renormalized spin wave excitations in a HEISENBERG ferromagnet including dipolar coupling, the parallel pumping effect under special considering the nonlinear three magnon interaction are discussed.
Abstract: Based on equations, symmetry and boundary conditions of quantum statistical correlation functions of renormalized spin wave excitations in a HEISENBERG ferromagnet including dipolar coupling, the parallel pumping effect under special considering the nonlinear three magnon interaction is discussed. An asymptotic approximation procedure enables us to interpret the fundamental equations in terms of the LANGEVIN theory of BROWNian motion and to find solutions by seperation ansatzes. For all cases of practical interest, the differences between the classical and the quantum statistical threshold condition can be neglected. The validity of SCHLOMANN'S subthreshold χ″ formula is proved. Above the threshold, the steady state χ″ is larger than proposed by semiclassical theories because the strongly excited spin waves are influenced by a certain nonlinear fluctuating field; for YIG, a sufficient agreement between experimental and theoretical χ″ values and a qualitative explanation of the parameter dependence are found. Some non-equilibrium correlation functions are given explicitly.
TL;DR: In this article, a model was proposed in which two spin-wave modes are coupled via one and two-magnon processes, and the amplitude of the non-uniform spinwave mode was calculated through the third order in the applied field.
Abstract: In an ordered magnetic system the imaginary part of the susceptibility declines at a much lower signal level than is predicted by the usual linear theory of magnetic resonance. This phenomenon is called premature saturation and is due to the parametric amplification of nonuniform spin‐wave modes which are degenerate with the uniform mode. In order to explain this phenomenon a model is proposed in which two spin‐wave modes are coupled via one‐ and two‐magnon processes. This system is treated by the method of time dependent Green's functions. Even in the lowest‐order approximation several types of two‐, three‐, and four‐time Green's functions must be calculated. Relations between these Green's functions are investigated, and then the amplitude of the nonuniform spin‐wave mode is calculated through the third order in the amplitude of the applied field. A criterion for the onset of parametric amplification is found and comparison is made with previous semiclassical treatments.