Quantum Mechanical Point Of View Research Articles

A quantum mechanical point of view to perturbative problems in classical mechanics

In this article it is shown that perturbative methods currently exploited in quantum mechanics can be used to treat a classical Liouville problem describing the evolution of an ensemble of noncollisional particles. The method discussed is based on the concepts of an evolution operator and interaction picture, which can be introduced for a classical Hamiltonian in full analogy with quantum mechanics. The usefulness of the developed method to treat the quantum extension of the Liouville equation is also stressed.

Classical and quantum study of a generalized Kepler–Coulomb system

AbstractThe nonrelativistic potential V = α/r + β cos θ/(r sin θ)2 + γ/(r sin θ)2, which constitutes an extension of the Kepler‐Coulomb potential and of the Hartmann potential, is investigated from both a classical and a quantum mechanical viewpoint. The corresponding Schrödinger equation is solved in parabolic coordinates by using the Kustaanheimo‐Stiefel transformation. The accidental degeneracy for the discrete spectrum is explained through the introduction of an su(2) dynamical invariance algebra. The Hamilton–Jacobi equation is solved in parabolic coordinates. The planarity and the periodicity of the trajectories are investigated. All finite trajectories are found to be quasi‐periodic (rather than periodic as in the case of the Kepler–Coulomb system). © 1993 John Wiley & Sons, Inc.

Čerenkov resonances and the Casimir geometry

The power spectrum of Čerenkov radiation off a charged particle is calculated in the Casimir geometry defined by two perfectly conducting neutral parallel plates with an isotrpic permeable medium trapped in between. An explicit analytic expression is obtained for the spectrum exhibiting resonances as a function of the geometry. A numerical analysis of the spectrum is also given for water trapped between the plates and the resonant frequencies are calculated. The analysis is given from a quantum mechanical viewpoint.

Quantum Mechanics and Superconductivity in a Magnetic Field

The influence of a magnetic field on superconductivity is usually described either phenomenologically, using Ginzburg-Landau theory, or semiclassically, using Gor'kov theory. In this article we discuss the influence of magnetic fields on the mean-field theory of the superconducting instability from a completely quantum-mechanical point of view. The suppression of superconductivity by an external magnetic field is seen in this more physically accurate picture to be due to the impossibility, in quantum mechanics, of precisely specifying both the centre-of-mass state of a pair and the individual electron kinetic energies. We also discuss the possibility of novel aspects of superconductivity at extremely strong magnetic fields, where recent work has shown that the transition temperature may be enhanced rather than suppressed by a magnetic field and where a quantum treatment is essential.

The chemical bond and molecular structure

Since Coulson's Tilden Lecture in 1951 there have been many developments in ideas about the chemical bond and about molecular structure. One aspect of those developments is considered here from a quantum mechanical standpoint. The conclusion reached is one of qualified pessimism about the extent to which it is possible to account for bonding and molecular structure (as perceived by the working chemist) from a quantum mechanical point of view.

Classical free-electron lasing in an undulating electrostatic field in the axial direction

It is shown that the phase of the electromagnetic wave emitted through stimulated emission is intrinsically random. The insensitivity of the phase of the laser field to any disturbance in the laser cavity parameter derives from the fact that stimulated and spontaneous emissions take place concurrently at the same wave vector, the phases of spontaneous emission are mildly bunched, and the central limit theorem can be applied to the phase of the laser field. The two spectral lines observed in the Smith-Purcell free-electron laser experiment show that both classical and quantum-mechanical free-electron lasings, in which the wigglers behave as classical waves and wiggler quanta respectively, take place concurrently at different laser wavelengths in the case of the electric wiggler. It is shown that the coherence of the classical free-electron laser is achieved through modulation of the relativistic electron mass by the electric wiggler. The classical free-electron lasing is calculated using the quantum-augmented classical theory. In this, the probability of stimulated emission is first evaluated by interpreting the classically derived energy exchange between an electron and the laser field from a quantum-mechanical viewpoint. Then the laser gain is obtained from this probability by using a relationship between the two quantities derived by quantum kinetics. The wavelength of the fundamental line of classical free-electron lasing is twice the wavelength of the fundamental line of the free-electron two-quantum Stark emission, which is the quantum free-electron lasing in the electric wiggler. The gain of the classical free-electron lasing appears to scale as λ3w/γ3, where γ is the Lorentz factor of the electron beam and λw is the wavelength of the wiggler.

Bianchi I cosmological model and the no-boundary condition

A study of the Bianchi I cosmological model is done from both the classical and quantum mechanical points of view. The field equations and their solutions are discussed in the classically forbidden region and classical region. Also the noboundary wave function is evaluated using the concept of microsuperspace and the Hawking-Hartle proposal.

Čerenkov-like radiation from a nambu string

We analytically calculate the Cerenkov radiation from a closed string arising from the Nambu action as a solution of a circularly oscillating closed string in an isotropic, permeable medium with index of refraction\(\sqrt {\mu \varepsilon } \). A numerical analysis of the expression is also given. The problem is treated from a quantum-mechanical viewpoint.

Laser Field Effects on the Transport Phenomena: Energy Loss,Stopping Power and Inverse Bremsstrahlung Process

The energy loss method has been applied to a large variety of transport problems in optics, solid state and fusion research. Usually, the transport equations are linearized, so they cannot deal with the multiphoton interaction in the presence of an intense laser field. In particular, not much attention has been given to collective contribution to the rates of the energy loss, stopping power and inverse Bremsstrahlung process from a quantum mechanical viewpoint. On the basis of the center of mass approach, we show the proper way to calculate the collective part of these rates. We report, for the first time in literature, some numerical calculations of these processes at resonant region for large values of the fast particle speed as compared to the electron thermal velocity (υ i /υ t ≫1).

Electromagnetic radiation from a Nambu string at finite temperatures

We determine the power of radiation from a closed string arising from the Nambu action as a solution of a circularly oscillating closed string atfinite temperatures. The problem is treated from a quantum-mechanical viewpoint.

Ab initio study on the transition state of acylation step of trypsin catalysis.

The transition state of acylation step of trypsin catalysis was determined by molecular orbital calculations. The calculations were carried out at the RHF-LCAO-SCF approximation level with double zeta basis set (plus polarization functions). The role of His57 residue in the acylation step of the catalytic reaction of trypsin was analysed from a quantum mechanical point of view. The influences of surrounding residues, such as oxyanion hole and Asp102-, and the electrostatic effect of the other regions of the enzyme were also studied. His57 was proved to capture the proton from Ser195 side chain terminus with its lone pair and to transfer it to substrate with electrostatic assistance of Asp102- and oxyanion hole.

Second-harmonic generation on simple metal surfaces: A quantum-mechanical point of view.

Second-harmonic generation was studied with quantum mechanics. The explicit form of the nonlinear current was derived for the high-frequency regime. The efficiency of second-harmonic generation was also discussed. A nonlinear surface-plasmon mode was found.

Quantum effects in a nonlinear coherent coupler

A nonlinear coherent coupler is discussed from the quantum-mechanical point of view, under the assumption that linear coupling between waveguides is strong enough. Such effects as quantum revivals, quantum intensity modulation, and squeezing are examined. Some results are compared with known experimental data.

Resonant and non-resonant tunneling in [formula omitted] multi quantum well structures

Transport experiments on electrons in coupled GaAs/AlAs multi quantum wells in an electric field perpendicular to the layers are reported. Under stationary conditions, structures in the field dependent photocurrent are observed. These structures are associated with an enhancement of the transport rates due to resonant tunneling). We further investigate the transient photocurrent and present time-of-flight experiments which allow to directly determine the transport times. We relate these transport data to the energetic spacings between the conduction subbands which are independently determined both experimentally (photocurrent spectroscopy) and theoretically (two-band approximation). We also discuss the temperature dependence of the transport times and present some model calculations. At low electric fields we observe transport effects in connection with miniband conduction and field induced localization. Finally, we study the influence of a transverse magnetic field on the transport characteristics and explain the results from a quantum mechanical point of view.

Plasma heating by two laser fields.

The heating of a plasma by electrons in the simultaneous presence of weak and strong laser fields by the inverse bremsstrahlung process is considered from a quantum-mechanical viewpoint. A kinetic equation is derived and the change in kinetic energy of the plasma electrons is calculated. Results show that the joint action of the two laser beams gives a nonvanishing but large heating rate in the regime of high intensity of the strong field. A physical explanation for this behavior is provided.

Stochastic dynamics of hydrogenic atoms in the microwave field: modelling by maps and quantum description

The motion of an electron of a classical hydrogenic atom in an oscillating electric field is studied theoretically. An analysis is provided, based on the iterative (mapping) forms of the classical equations of motion in perturbation theory and the adiabatic approximation. This greatly facilitates the numerical investigation of stochasticity and the ionisation process and allows the approximate analytical estimation of the threshold field strengths for the onset of chaos and of the diffusion coefficient of the electron in energy space. The method is asymptotically exact at high field frequencies and gives a good approximation for medium and low frequencies. The adiabatic approximation describes well the approach of the stochastic ionisation threshold field strength to the static field ionisation threshold. From the quantum mechanical point of view the ionisation is a result of the great number of one-photon transitions in the strongly perturbed spectrum of the atom. This results in the diffusion of the electron in energy space identical to the diffusion due to stochastic classical motion. The estimation of the mean time of diffusive ionisation is also given.

Motion of a particle in a Coulomb plus Aharonov-Bohm potential

The motion of a particle in a Coulomb plus Aharonov-Bohm potential is investigated from a classical and a quantum mechanical viewpoint. The quantum bound states are derived by using the KS transformation. The grouping of certain levels is explained via the introduction of an SU (2) dynamical algebra. All classical finite ttrajectories are found to be periodic.

Far-infrared absorption by small metallic particles in a spherical oscillator well

We examine, from the quantum-mechanical point of view, the vibrational motion of small metallic particles contained in amorphous materials and its contribution to the far-infrared absorption by these composite media. Temperature effects are considered. The results are discussed and compared with experimental data.

Nonresonant wave-particle interaction in semiclassical quasilinear theory.

A nonresonant nature of wave-particle interaction is clarified from the viewpoint of quantum mechanics. The interaction of particles and quasiparticles can be described by the use of transition probability which is found to have both resonant and nonresonant contributions. The resonant transition probability is known as Fermi's golden rule, which is now supplemented by the nonresonant contribution, resulting in the proper conservation of energy and momentum in the particle-quasiparticle system.

Responses of bristle field sensilla inApis mellifica to geomagnetic and astrophysical fields

The response of a bristle field sensillum inApis mellifica may be described as follows. 1. Distinct artificial magnetic fields (especially tilting of the static vector) influence the impulse frequency of the sensory cell. 2. At certain hours of the day characteristic changes of the impulse frequency occur. 3. Under predominantly natural magnetic field (MF) conditions there are significant correlations between the variation of selected MF components and impulse frequency (IMP). However, when a spatially oscillating MF-vector is applied, the IMP course does not always show a formal coincidence with MF variation. 4. Our hypothesis is that in this case the trigonometric constellation of sun (S) and moon (M) becomes the dominant guiding factor. 5. IMP frequency — with a given total azimuthal shift of the SM-system — may be calculated by the following equation using S and M azimuth and height data: $$IMP_{freq} = \pm (0.46 \cdot (\sin Az_S + \sin h_S ) + (sin Az_M + \sin h_M ))/\Delta t$$ Az=azimuth (in angular degrees),h=height (in angular degrees). 6. A quantization of the space in 90° steps and the preference of the north-south direction in this orientation system are evident. MF influences are discussed in relation to nuclear magnetic resonance; effects caused by the sun-moon constellation seem to be a gravitational modulation. A partial synthesis of both parameters is possible. Those results are discussed from a quantum mechanical point of view.