Bohmian interpretation

Whereas linear momentum in the Bohmian interpretation relates to the translation of wavefronts (p = VS), angular momentum is described by their rotation. The components of angular momentum along a space direction (z-axis) are defined in a central field (e.g. hydrogenic atom) by 

For given t and me / 0, the wavefronts S — constant, are planes parallel to, and ending on the z-axis with starting values ro0o(j)o as in figure 5. (z is a nodal line of tr when me 0). 

As t increases the planes rotate anticlockwise about the z-axis with angular velocity Q, = f = E/meh, as shown in figure 6. As the phase changes 

The wavefronts for different values of m are shown in figure 6. The particle (charge) orbits the z-axis along a circle of constant radius (p0 = r0 sin 0), which is not fixed as in the old Bohr theory. The wavefronts of states for which me 0 rotate clockwise. 

The number of rotating planes corresponds to mi. For m = 0 the wave function (16) is real. In a spherically symmetrical environment there is no special direction in space and the wave function (18) acquires geometrical meaning only when an external magnetic field is switched on. Any of the 

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As in the hydrodynamic model the Bohmian interpretation assumes a wave function in polar form,... 

The most revolutionary consequence of the Bohmian interpretation of orbital angular momentum is perhaps the natural interpretation of non-steric molecular barriers to rotation and the nature of multiple bonds. It completely destroys the notion of 7r-bonding and explains the absence of a barrier to rotation in bonds of odd integer order. 

The distinction between classical and non-classical descriptions of a system should not be confused with the classical and non-classical behaviours of a single system that become identical in the classical limit of the Bohmian interpretation. The unacceptable procedures outlined above amount to extrapolation of the classical description into the non-classical domain, beyond the limit, to where it has no validity. 

Bohmian mechanics refers to the ontological interpretation of quantum theory pioneered by Bohm [4]. The mathematical structure of the theory is not affected by the different interpretation and the same formalism adopted before [7] will be used here. 

Some of the chemical concepts with little or no quantum-mechanical meaning outside the Bohmian formulation but, well explained in terms of the new interpretation, include electronegativity, the valence state, chemical potential, metallization, chemical bonding, isomerism, chemical equilibrium, orbital angular momentum, bond strength, molecular shape, phase transformation, chirality and barriers to rotation. In addition, atomic stability is explained in terms of a simple physical model. The central new concepts in Bohmian mechanics are quantum potential and quantum torque. 

Bohmian formalism provides a much clearer link to chemical phenomena than the conventional interpretation. The remainder of this book concentrates on this topic. 

The quantum potential can now be identified as a surface effect that exists close to any interface, in this case the vacuum interface. The non-local effects associated with the quantum potential also acquire a physical basis in the form of the vacuum interface, now recognized as the agent responsible for mediating the holistic entanglement of the universe. The causal interpretation of Bohmian mechanics finds immediate support in the postulate of a vacuum interface. There is no difference between classical and quantum entities, apart from size. Logically therefore, the quantum limit depends on... 

The chemistry community, understandably, failed to respond at all, even though Bohmian mechanics probably holds the key to the development of a theory of chemistry, soundly based on quantum theory and relativity. The problem with molecular structure is resolved by the ontological interpretation of quantum-mechanical orbital angular momentum and the key to chemical reactivity and reaction mechanism is provided by the quantum potential function. 

The contentious issue of quantum-particle trajectories is put into perspective by the Bohmian model. One interpretation is that the quantum electron has an unspecified diffuse structure, which contracts into a classical point-like object when confined under external influences. The observed trajectory, as in a cloud chamber, may be considered to follow the centre of gravity. 

This suggests that to determine the path solutions in Eq. (4.88), j4(R, t) should be known beforehand. This is a nonlinear process. However, the Bohmian dynamics is known to be a very important reformulation of the Schrodinger equation with respect to the interpretation of quantum mechanics. Much study has been devoted to practical methods to numerically realize the Bohmian dynamics in the context of chemical dynamics (see [48f] and references therein). 

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