Quantum/classical potential balance

Nevertheless, the above quantum-classical force balance in chemical interaction at the level of forces can be further specialized at the level of chemical action functional which is nothing else than the observable of the potential involved it provides the entangled equation of the electronic density. 

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 individual sectors of a factorizable product-state system are partially holistic and appropriate to describe molecules. Each sector of this type has a characteristic quantum potential that keeps it together by balancing the classical potential. A molecule may therefore be viewed as a chemical entity made up of particles that move under the influence of a common quantum potential. 

The discovery of quantum mechanics was seen as a dramatic departure from classical theory because of the unforeseen appearance of complex functions and dynamic variables that do not commute. These effects gave rise to the lore of quantum theory as an outlandish mystery that defies comprehension. In our view, this is a valid assessment only in so far as human beings have become evolutionary conditioned to interpret the world as strictly three dimensional. The discovery of a 4D world in special relativity has not been properly digested as yet, because all macroscopic structures are three dimensional. Or, more likely, minor discrepancies between 4D reality and its 3D projection are simply ignored. In the atomic and molecular domains, where events depend more directly on 4D potential balance, projection into 3D creates a misleading image of reality. We argue this point on the basis of different perceptions of chirality in 3D and 2D, respectively. 

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. 

Methods relying on parametrised potential functions for the description of energy hypersurfaces are commonly referred to as molecular mechanics (MM) or classical mechanics and these methods have a long tradition in computational chemistry. Entire data sets of balanced potential functions and their respective parameters are referred to as force fields [23,24,25], The key advantage of MM methods is the low computational demand compared to quantum mechanical computations. 

The acceleration of the particle by the quantum potential — Wq/m balances the classical acceleration W/m so that the particle remains in a fixed position and is prevented from falling into the nucleus by the outward acceleration due to the quantum potential. 

Unless demanded by symmetry, the value of will not be an extremum at a critical point in p. Thus, the critical points in V and p will not, in general, coincide and the distribution of eleetronie eharge, even in a one-electron system, is not determined entirely by the external foree — V V t). Bohm (1952) ascribed the stability of a stationary state in a quantum system to the balance between the classical force —W and the quantum mechanical force which is given by the gradient of the quantum potential . For a one-electron system at a critical point in p(r), Bohm s quantum mechanical force is just the right-hand side of eqn (3.8). The Laplacian of the charge density, the quantity appearing in the quantum potential, is an important local property of a system and is the subject of Chapter 7. 

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