Three-space from quantum mechanics

We formulate a discrete quantum-mechanical precursor to spacetime geometry. The objective is to provide the foundation for a quantum mechanics that is rooted exclusively in quantum-mechanical concepts, with all classical features, including the three-dimensional spatial continuum, emerging dynamically.     

Relationships between Electrodynamic and Quantum-Mechanical Parameters in the Theory of Quantum Transitions

Relationships between the electrodynamic (wave propagation constants) and quantum-mechanical parameters (probability of induced transitions) of interaction between energy quanta and particles of the medium are derived for dipole and paramagnetic interaction types. It is demonstrated that quantum-mechanical parameters are generally complex.     

Relativistic kinetic theory of quantum systems: III. Transport equation for a neutrino system

On the basis of the quantum-mechanical equations of motion and the statistical assumption that dynamical correlations present in the initial state may be ignored, a kinetic equation for a dilute neutrino system is derived. If the system is sufficiently uniform in space this equation reduces to the relativistic Boltzmann equation for massless particles with a quantum-mechanical transition probability.     

Quantum mechanics and mechanical properties: Towards twenty-first century materials

The use of materials with otherwise attractive properties is often limited by unacceptable mechanical performance. Fortunately, modern processing techniques are sometimes able to overcome such deficiencies, though a systematic and fundamental approach to materials development has yet to be devised. Recent advances in quantum-mechanical computational capabilities have fostered a growing number of applications that bear directly upon the mechanical properties of materials. After a brief discussion of the role of defect structures in mediating deformation behaviour, techniques for computing properties of solids within a quantum-mechanical framework are reviewed. Examples are cited where insight into macroscopic behaviour has been attained from the application of quantum-mechanical calculations to materials of technological importance.     

Algorithm for solving the inverse vibronic problem on the basis of SVL fluorescence spectra

Computer methods whereby the inverse vibronic problem is solved on the basis of resonance fluorescence spectra with the use of modern quantum-mechanical methods for constructing structuraldynamic models of polyatomic molecules are discussed. An algorithm is proposed for solving the inverse vibronic problem according to resonance fluorescence spectra under laser excitation, and the corresponding calculation programs are constructed. The initial program data are acquired by means of an original software package which implements the scaling of quantum-mechanical force fields in two electronic states. The Duschinsky matrix and the initial matrix of shifts in normal coordinates caused by electron excitation are calculated in the Cartesian and natural vibrational coordinates. The program data are taken from quantum-molecular models based on calculations performed via ab initio modern quantum-mechanical methods and density functional theory. The algorithm is tested through the calculation of a model molecular system.     

Renormalization of the inverse square potential

The quantum-mechanical D-dimensional inverse square potential is analyzed using field-theoretic renormalization techniques. A solution is presented for both the bound-state and scattering sectors of the theory using cutoff and dimensional regularization. In the renormalized version of the theory, there is a strong-coupling regime where quantum-mechanical breaking of scale symmetry takes place through dimensional transmutation, with the creation of a single bound state and of an energy-dependent s-wave scattering matrix element.     

Coupled physical systems

The purpose of this paper is to sketch an attack on the general problem of representing a composite physical system in terms of its constituent parts. For quantum-mechanical systems, this is traditionally accomplished by forming either direct sums or tensor products of the Hilbert spaces corresponding to the component systems. Here, a more general mathematical construction is given which includes the standard quantum-mechanical formalism as a special case.Dedicated to Professor Peter Mittelstaedt.     

Analogs of de Finetti's theorem and interpretative problems of quantum mechanics

It is argued that the characterization of the states of an infinite system of indistinguishable particles satisfying Bose-Einstein statistics which follows from the quantum-mechanical analog of de Finetti's theorem ⁽²⁾ can be used to interpret the nonuniqueness of the resolution into a convex combination of pure states of a quantum-mechanical mixed state.     

Recursion operators, higher-order symmetries and superintegrability in quantum mechanics

A connection between the theory of superintegrable quantum-mechanical systems, which admit a maximal number of integrals of motion, and the standard Lie group theory is established. It is shown that the flows generated by first- and second-order Lie symmetries of the bidimensional Schrödinger equation can be classified and interpreted as quantum-mechanical operators which commute with integrable or superintegrable Hamiltonians. In this way, all known superintegrable potentials in the plane are naturally obtained and slightly more general integrals of motion are found.     

"Learn on the fly": a hybrid classical and quantum-mechanical molecular dynamics simulation

We describe and test a novel molecular dynamics method which combines quantum-mechanical embedding and classical force model optimization into a unified scheme free of the boundary region, and the transferability problems which these techniques, taken separately, involve. The scheme is based on the idea of augmenting a unique, simple parametrized force model by incorporating in it, at run time, the quantum-mechanical information necessary to ensure accurate trajectories. The scheme is tested on a number of silicon systems composed of up to approximately 200 000 atoms.     

Photodetachment cross section of S^- in electric and magnetic fields＊

In this paper, the quantum-mechanical photodetachment cross section of S^- in uniform electric and magnetic fields at arbitrary angles is presented. It compares the quantum-mechanical cross section with the quantum source formalism cross section. The results show that at large angle, the two results have good agreements, however, with the decrease of the angles, they deviate obviously from each other. The reasons for this discrepancy are also discussed.     

Reservoir as a source of probability in quantum mechanics

The concept of the theory of measurement and choice of quantum alternative is considered, according to which the outcome of a particular measurement is determined by the reservoir (detector) state. The way of deducing standard (probabilistic) quantum-mechanical interpretation rules is discussed, with special emphasis on the theoretical demonstration of the wave-function reduction phenomenon. The method of resolving the “Schrodinger cat” paradox is suggested. The interrelation between the mechanisms of formation of shot and flicker noises and the role of reservoir in the formation of quantum-mechanical probability is discussed.     

以两种方法研究强激光场中的非时序双电离现象

以半经典再散射模型和量子S矩阵模型出发来研究强激光场中原子和分子的非时序双电离现象.分别利用这两个模型计算了电离率随激光强度的变化、反冲离子的动量分布、两出射电子的能量分布.数值结果表明半径典再散射模型和量子S矩阵模型在研究强场中原子和分子的非时序双电离现象时有很好的一致性.     

Strong-coupling approximations

Standard path-integral techniques such as instanton calculations give good answers for weak-coupling problems, but become unreliable for strong-coupling. Here we consider a method of replacing the original potential by a suitably chosen harmonic oscillator potential. Physically this is motivated by the fact that potential barriers below the level of the ground-state energy of a quantum-mechanical system have little effect. Numerically, results are good, both for quantum-mechanical problems and for massive φ⁴ field theory in 1+1 dimensions.     

PREPARATION OF TWO-MODE NONCLASSICAL STATES IN AN ION TRAP BY A QUANTIZED LASER BEAM

Based on the former quantum-mechanical study on the effective harmonic trap confining an ultracold ion, we make a quantum-mechanical treatment for the radiation field of the laser. Thus some two-mode nonclassical states, i.e., an approximate two-mode squeezed state and different two-mode entangled Fock states can be prepared in the red- and blue-detuning cases, respectively, within Lamb-Dicke regime and strong confinement limit.     

Analysis of the two-photon absorption spectrum of benzonitrile based on the direct quantum-mechanical calculation of the intensity distribution

A direct quantum-mechanical calculation of the intensity distribution in the two-photon absorption spectrum of benzonitrile is performed taking into account the Herzberg-Teller effect. The excitation mechanism of all the observed lines, including lines corresponding to the excitation of single-quantum nontotally symmetric vibrations and their combinations with totally symmetric modes, is analyzed. The results of the calculation, performed taking into account the frequency effect and the Duschinsky effect, agree satisfactorily with experimental data. This indicates that it is worthwhile to apply the quantum-mechanical method in calculations of the intensity distribution in the two-photon absorption spectra of cyclic molecules.     

The impossibility of complete mutual observation

It is pointed out that two quantum-mechanical physical systems cannot simultaneously observe each other completely.