Superposition Of Wave Functions Research Articles

Stochastic bra-ket interpretation of quantum mechanics

Abstract The stochastic nature of quantum mechanics is more naturally reflected in a bilinear two-process representation of density matrices rather than in squared wave functions. This proposition comes with a remarkable change of the entanglement mechanism: entanglement effects do not originate from superpositions of wave functions, but they result from the bilinear structure of density matrices. Quantum interference appears as a multiplicative phenomenon rather than an additive superposition mechanism. We propose two general requirements such that the bilinear representation of density matrices is given in terms of two uniquely defined, identically distributed, Markovian stochastic jump processes. These general ideas are illustrated for the Einstein-Podolsky-Rosen and double-slit experiments. The expression of the stochastic nature of quantum mechanics in terms of random variables rather than their probability distributions facilitates an ontological viewpoint and leads us to a bra-ket interpretation of quantum mechanics.

Superposition of Wave Functions in the G-Qubit Theory

Quantum computing rests upon two theoretical pillars: superposition and entanglement. But some physicists say that this is a very shaky foundation and quantum computing success will have to be based on a different theoretical foundation. The g-qubit theory supports that point of view. Current article is the first one of two and about the superposition principle. Quantum superposition principle states that any two quantum wave functions can be superposed, and the result be another valid wave function. It specifically refers to linearity of the Schrodinger equation. In the g-qubit theory quantum wave functions are identified by points on the surface of three-dimensional sphere . That gives different, more physically feasible, not mysterious, explanation of what the superposition is.

Mechanisms of Modulation Formation in Elastic Diffraction Scattering of Charged Particles

In this work, the authors describe experimental data on the angular distributions of alpha particles on light alpha-cluster nuclei. The angular distributions of elastic scattering of alpha particles are analyzed under the assumption of complete absorption inside the sphere of the cluster structure and the sphere of the interaction core. These assumptions made it possible to decompose the scattering amplitude into components—scattering on the nucleus itself and on different cluster structures. The calculations result in the following. The amplitude for describing diffraction elastic scattering by 4n ± 1 light nuclei in the framework of the theory of diffraction scattering is a superposition of wave functions in the scattering approximation on a completely black core and on its absolutely black substructures. The nucleon association modes, as well as the scattering modes on the correlated motion of nucleons and spatially separated nucleons, make a significant contribution to the total scattering amplitude. This manifests itself as an increase in angular distributions due to the interference of modes of various cluster structures and nucleons. Owing to these effects, not only an uneven rise in the angular distributions of differential cross sections over the Rutherford section is possible, but also a rise at rear angles.

Spin precession as a consequence of the quantum spin-flip transitions with a non-stationary wave function

In this work, a precise quantum analog of spin precession of classical theory is obtained. As an example, a neutral Dirac particle (neutron) is considered. A non-stationary wave function is a superposition of wave functions with counter spins. It is used to calculate the average value of the spin operator. It is demonstrated that classical and quantum theories lead to an adequate description of the spin precession.

Photodissociation of group-6 hexacarbonyls: observation of coherent oscillations in an antisymmetric (pseudorotation) vibration in Mo(CO)5 and W(CO)5

On dissociation of M(CO)(6), M = Cr, Mo and W, by a femtosecond UV laser (<270 to 360 nm), pronounced coherent oscillations are observed in the pentacarbonyl products on probing by long-wavelength (810 nm) ionization in the gas phase. They are vibrations in the ground state, driven by the slope from a conical intersection on relaxation from the initially formed excited state (S(1)). Surprisingly, with M = Mo and W we also find a fundamental of an antisymmetric (b(2) in C(4v)) vibration. From positive and negative displacements along such a coordinate one would expect the same signal, so that there should be only overtones. Vibrational selection rules are therefore considered for time-resolved spectroscopy. The reason for the symmetry breaking is suggested to result from the fact that the phase in superposition of wave functions is established by the pump process and this phase is conserved in probing, independently of the probe delay. An antisymmetric fundamental can be observed, if there is a small tunneling splitting in a state involved in the probe process. The observations also imply some conclusions on the dissociation and relaxation processes and the potentials: with longer wavelengths, the wave packet enters on the same surface but from a different direction to S(1). Only a very minor fraction of the available energy appears as coherent oscillation. There is no equipartition at the end, and a second CO is cleaved off in few picoseconds, even if there is only very little excess energy. Triplets do not contribute, even in the tungsten system and at longest wavelengths. The dissociation mechanism involves passage of the wave packet from all initial states over an avoided crossing to a repulsive ligand-field surface. It predicts that in some other molecules, the barrier caused thereby is larger and for long photolysis wavelength the lifetime is long enough for intersystem crossing to take place; it also predicts wavelength dependences in these cases. It is again emphasized that there is no vertical internal conversion; instead, the molecule is controlled by slopes and intersections of potentials. Also lifetimes can be considered as a control parameter in photochemistry.

CLUSTER STRUCTURES IN 28Si

Positive-parity states of 28 Si are studied with antisymmetrized molecular dynamics and multi-configuration mixing focusing on clustering and deformations. By superposition of wave functions obtained by energy variation imposing constraints on quadrupole deformation parameter β and distance between α and 24 Mg , and 12 C and 16 O clusters, two oblate bands, two prolate bands and developed α-24 Mg band are obtained. It is found that cluster structure components are contained in those bands.

Superselection from canonical constraints

The evolution of both quantum and classical ensembles may be described via the probability density P on configuration space, its canonical conjugate S, and an_ensemble_ Hamiltonian H[P,S]. For quantum ensembles this evolution is, of course, equivalent to the Schroedinger equation for the wavefunction, which is linear. However, quite simple constraints on the canonical fields P and S correspond to_nonlinear_ constraints on the wavefunction. Such constraints act to prevent certain superpositions of wavefunctions from being realised, leading to superselection-type rules. Examples leading to superselection for energy, spin-direction and `classicality' are given. The canonical formulation of the equations of motion, in terms of a probability density and its conjugate, provides a universal language for describing classical and quantum ensembles on both continuous and discrete configuration spaces, and is briefly reviewed in an appendix.

One more note about the ionicity scale of Pauling

It is suggested that the ionicity scale derived from thermochemical data by Pauling may characterize the covalent and ionic contributions to the bond in a better approximation, if combination of these two contributions are considered as a superposition of charges (mixed state) rather than a superposition of wave functions.

Waves generated in the configuration of a magnetically confined and field-permeated axisymmetric jet

A cylindrical MGD configuration comprising an electrically conducting, infinitely extended (cylindrical) jet which is both permeated and contained by stream-aligned magnetic fields is considered. Axisymmetric perturbations are then generated by exposure to a stationary, weak, azimuthal current source. Ignoring relativistic and dissipative effects, asymptotic solutions complying with a radiation condition are established for the steady state. Generally speaking, the disturbed system propagates a discrete superposition of wave functions, each of which is uniquely obtained for either the upstream or downstream region. In the non-trivial cases, there is no axial wave attenuation. However, transverse attenuations are experienced within the fluid-free enveloping field. The various jet-flow regimes are thoroughly examined. It is found, in particular, that a single stationary wave is produced upstream wheneverM&lt; 1,M2+A2[ges ] 2 and λβ &lt; 1, while ifM&gt; 1 andA&gt; 1 an infinity of discrete stationary waves occurs downstream.MandAbeing, respectively, the Mach and Alfvén numbers of the jet; λβ is a parameter involvingM, AandA0(an interface Alfvén number).