Quantum torque

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. 

The second term on the left in (20) is explained as a quantum torque not associated with the motion and although L2 = 0 for a stationary particle, the angular momentum may be non-zero, as in a pz-state [35]. Although the electron has angular momentum in three dimensions the projection thereof on an axis, is zero. The quantum torque can therefore not be due to rotation about an axis and arises from spherical rotation about a point, to be described in chapter 4.7. 

Like its energy, the angular momentum of the valence electron also becomes spherically averaged. It rotates in spherical mode and its total angular momentum appears as quantum torque. Like a spinning electron this orbital quantum torque sets up a half frequency wave field that resonates non-locally with the environment. The most general solution to the wave equation of a spherically confined particle therefore is the Fourier transform of the spherical Bessel function... 

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... 

To understand this, and other intramolecular rearrangements, it is necessary to give up the naive notion of Lewis-type electron-pair bonds. The alternative is to view all interaction within a partially holistic molecule as mediated by its quantum potential and quantum torque. Both of these quantities are specified by the total molecular wave function. The necessary theory for this approach has not been worked out. 

There is no evidence that any classical attribute of a molecule has quantum-mechanical meaning. The quantum molecule is a partially holistic unit, fully characterized by means of a molecular wave function, that allows a projection of derived properties such as electron density, quanmm potential and quantum torque. There is no operator to define those properties that feature in molecular mechanics. Manual introduction of these classical variables into a quantum system is an unwarranted abstraction that distorts the non-classical picture irretrievably. Operations such as orbital hybridization, LCAO and Bom-Oppenheimer separation of electrons and nuclei break the quantum symmetry to yield a purely classical picture. No amount of computation can repair the damage. 

The K quantum number ean not ehange beeause the dipole moment lies along the moleeule s C3 axis and the light s eleetrie field thus ean exert no torque that twists the moleeule about this axis. As a result, the light ean not induee transitions that exeite the moleeule s spinning motion about this axis. 

This effect can in principle be measured by any technique that is sensitive to the magnetisation dynamics and in addition to the SQUID measurements above quantum tunnelling of magnetisation (QTM) has been observed for Mni2 by, for example, torque magnetometry, and Mn nuclear relaxation rates in and specific heat. ... 

Fig. III.7. The selection rules JM = 0 or JM = 1 niay be selected by changing the orientation of the rectangular waveguide cell within the gap. In case a) the electrical vector of the incident microwave radiation being perpendicular to the broad face of the waveguide will produce no torque in the direction of the magnetic field which serves as the quantization axis. This geometry leads to the /iM = 0 selection rule. In case b) the same classical argument suggests /IMyi 0 (quantum mechanics leads to dM = 1)...

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