Quantum potential field

A system of this type is not holistic, but partially holistic, which means that pairwise interaction occurs between the holistic units. The distinction drawn here between holistic and partially holistic systems is not in line with the terminology used in general philosophic discourse and in order to avoid any confusion it is preferable to distinguish between systems that interact either continuously, or discontinuously, with the quantum potential field. Quantum potential, like the gravitational potential, occurs in the vacuum, presumably with constant intensity. The quantum potential energy of a quantum object therefore only depends on the wave function of the object. 

The archetype of quantum objects is the photon. It is massless, has unit spin, carries no charge, and responds to the quantum potential field. By comparison, an electron is a massive fermion with half-spin and unit negative charge. It responds to both classical and quantum potentials. The only property that these two entities have in common is their wave nature,... 

The appearance of a quantum-potential field is related to the gauge, or phase, transformation of a quantum wave. It is assumed that the wave field of a quantum object that moves through space suffers a change of phase, such that... 

Gauge fields (M) that restore local phase invariance are evidently closely related also to the quantum-potential field. The wave function of a free electron, with temporal and spatial aspects of the phase factor separated, may be written as... 

The previous conclusion immediately clarifies the mystery of non-local interaction through the space-like nature of the quantum potential field. All theories actually agree that superluminal motion occurs in the interior of the electron as first discovered by Dirac, but a non-local connection is not restricted to the interior of an electron it can occur in any region of high quantum potential, for instance in the interior of an atom or a small molecule. As the quantum potential is inversely proportional to mass, non-local interaction within more complex and more massive bodies becomes less significant. External classical potentials also have a disruptive influence on non-local interaction claims that such connections exist over galactic distances might be inflated, but within the domain of chemical reactions they must be of decisive importance. 

Next, imagine that the promoted atom is one of many, all similarly activated by a static field of applied pressure. All atoms are in the same valence state and interact non-locally through quantum torque and the quantum-potential field, which becomes a function of all particle coordinates. This... 

The interface between two liquid phases will differ from this construct in detail only. The postulated effects of a potential field that changes appreciably over the dimensions of interacting particles near the surface remain valid. In the case of the vacuum interface it is the quantum-potential field that causes the surface effects. 

Exploration of intramolecular non-local effects could be the beginning of more far-reaching studies. Neural receptors with the ability to exchange information via the quantum-potential field in the vacuum interface, could be another level of quantum object that might eventually explain para-psychic phenomena. 

Partial Least Squares (PLS) regression (Section 35.7) is one of the more recent advances in QSAR which has led to the now widely accepted method of Comparative Molecular Field Analysis (CoMFA). This method makes use of local physicochemical properties such as charge, potential and steric fields that can be determined on a three-dimensional grid that is laid over the chemical stmctures. The determination of steric conformation, by means of X-ray crystallography or NMR spectroscopy, and the quantum mechanical calculation of charge and potential fields are now performed routinely on medium-sized molecules [10]. Modem optimization and prediction techniques such as neural networks (Chapter 44) also have found their way into QSAR. 

Our presentation of the basic principles of quantum mechanics is contained in the first three chapters. Chapter 1 begins with a treatment of plane waves and wave packets, which serves as background material for the subsequent discussion of the wave function for a free particle. Several experiments, which lead to a physical interpretation of the wave function, are also described. In Chapter 2, the Schrodinger differential wave equation is introduced and the wave function concept is extended to include particles in an external potential field. The formal mathematical postulates of quantum theory are presented in Chapter 3. 

The first two chapters serve as an introduction to quantum theory. It is assumed that the student has already been exposed to elementary quantum mechanics and to the historical events that led to its development in an undergraduate physical chemistry course or in a course on atomic physics. Accordingly, the historical development of quantum theory is not covered. To serve as a rationale for the postulates of quantum theory, Chapter 1 discusses wave motion and wave packets and then relates particle motion to wave motion. In Chapter 2 the time-dependent and time-independent Schrodinger equations are introduced along with a discussion of wave functions for particles in a potential field. Some instructors may wish to omit the first or both of these chapters or to present abbreviated versions. 

The previous result is an important one. It indicates that there can be yet another fruitful route to describe lipid bilayers. The idea is to consider the conformational properties of a probe molecule, and then replace all the other molecules by an external potential field (see Figure 11). This external potential may be called the mean-field or self-consistent potential, as it represents the mean behaviour of all molecules self-consistently. There are mean-field theories in many branches of science, for example (quantum) physics, physical chemistry, etc. Very often mean-field theories simplify the system to such an extent that structural as well as thermodynamic properties can be found analytically. This means that there is no need to use a computer. However, the lipid membrane problem is so complicated that the help of the computer is still needed. The method has been refined over the years to a detailed and complex framework, whose results correspond closely with those of MD simulations. The computer time needed for these calculations is however an order of 105 times less (this estimate is certainly too small when SCF calculations are compared with massive MD simulations in which up to 1000 lipids are considered). Indeed, the calculations can be done on a desktop PC with typical... 

This formulation results very insightful according to Equation 8.30, particles move under the action of an effective force — We , i.e., the nonlocal action of the quantum potential here is seen as the effect of a (nonlocal) quantum force. From a computational viewpoint, these formulation results are very interesting in connection to quantum hydrodynamics [21,27]. Thus, Equations 8.27 can be reexpressed in terms of a continuity equation and a generalized Euler equation. As happens with classical fluids, here also two important concepts that come into play the quantum pressure and the quantum vortices [28], which occur at nodal regions where the velocity field is rotational. 

In the quantum-mechanical description of atoms and molecules, electrons have characteristics of waves as well as particles. In the familiar case of the hydrogen atom, the orbitals Is, 2s, 2p,... describe the different possible standing wave patterns of electron distribution, for a single electron moving in the potential field of a proton. The motion of the electrons in any atom or molecule is described as fully as possibly by a set of wave functions associated with the ground and excited states. 

Another thing to keep in mind is that most quantum chemistry calculations, by default, treat the molecules as gas-phase species in a vacuum. In contrast, most laboratory experiments are done in solvent. Today, fortunately, many of the widely used quantum chemistry programs have a way of approximating the effect of solvent on solute models. The solvent can be treated in two ways. Water is a common solvent, so we will use it as an example. One way is to use the so-called explicit waters in this approach, a few water molecules are sprinkled around the periphery of the solute to mimic the effect of a solvation shell or hydrogen bonding, and the whole ensemble is run in the calculation. The other way is to use implicit waters in which an average potential field that would be produced by water... 

The theory of chemical bonding is overwhelmed by a host of insurmountable obstacles the real orbitals and hybrids of LCAO have no physical, chemical or mathematically useful attributes - certainly not in the quantum-mechanical sense the distribution of electron density between atoms, in the form of spin pairs, is an overinterpretation of the empirical rules devised to catalogue chemical species the structures, assumed in order to generate free-molecule potential fields, are only known from solid-state diffraction experiments the assumption of directed bonds is a leap of faith, not even supported by crystal-structure analysis. The list is not complete. 

The electron which responds to both quantum and classical potential fields exhibits this dual nature in its behaviour. Like a photon, an electron spreads over the entire region of space-time permitted by the boundary conditions, in this case stipulated by the classical potential. At the same time it also responds to the quantum field and reaches a steady, so-called stationary, state when the quantum and classical forces acting on the electron, are in balance. The best known example occurs in the hydrogen atom, which is traditionally described to be in the product state tpH = ipP ipe, hence with broken holistic symmetry. In many-electron atoms the atomic wave function is further fragmented into individual quantum states for pairs of electrons with paired spins. 

The total energy of an electron in the potential field V of an atomic core tends to zero as V —> 0 on compression to ro- The calculated energy of the decoupled valence electron can therefore only arise from the quantum potential and it will be argued that this energy represents the concept, intuitively defined before as the electronegativity of an atom. The wave function (3.36) of the valence electron will be argued to determine the chemical interaction of an atom with its environment. 

The interacting waves from myriads of charge centres constitute the electromagnetic radiation field. In particle physics the field connection between balanced charge centres is called a virtual photon. This equilibrium is equivalent to the postulated balance between classical and quantum potentials in Bohmian mechanics, which extends holistically over all space. 

Entropy production during chemical change has been interpreted [7] as the result of resistance, experienced by electrons, accelerated in the vacuum. The concept is illustrated by the initiation of chemical interaction in a sample of identical atoms subject to uniform compression. Reaction commences when the atoms, compacted into a symmetrical array, are further activated into the valence state as each atom releases an electron. The quantum potentials of individual atoms coalesce spontaneously into a common potential field of non-local intramolecular interaction. The redistribution of valence electrons from an atomic to a metallic stationary state lowers the potential energy, apparently without loss. However, the release of excess energy, amounting to Au = fivai — fimet per atom, into the environment, requires the acceleration of electronic charge from a state of rest, and is subject to radiation damping [99],... 

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