Mechanics angular momentum

The components of the quantum mechanical angular momentum operators along the three principal axes are ... 

Any operator J, which satisfies the commutation rule Eq. (7-18), represents quantum mechanical angular momentum. Orbital angular momentum, L, with components explicitly given by Eq. (7-1), is a special example5 of J. 

The proof of the theorem affirming that J8 is a proper quantum mechanical angular momentum involves only an expansion of (Ji + J2) x (Ji + J2) with subsequent use of the commutation rules for Jj and J2, and the fact that Jj and J2 commute because they act in... 

Eigenstates of a crystal, 725 Eigenvalues of quantum mechanical angular momentum, 396 Electrical filter response, 180 Electrical oscillatory circuit, 380 Electric charge operator, total, 542 Electrodynamics, quantum (see Quantum electrodynamics) Electromagnetic field, quantization of, 486, 560... 

Bloch employed what chemists call the semiclassical model, where the motions of the projectile and the target nucleus are treated classically while target electrons obey quantum mechanics. In this model the impact parameter p refers to the target nucleus rather than an electron. In genuine quantum mechanics, angular momentum takes over the role of an impact parameter [9]. 

Such triples of operators are often called angular momentum operators or generators of angular momentum. Sometimes they are indeed related to actual mechanical angular momentum more often, the label angular momentum is the physicists way of saying that the operators satisfy the commutation relations given above. 

As we have seen (Section 4.1), the behavior of the angular momentum J in a magnetic field is determined by the collinear magnetic moment pbj coupled with it. It is therefore important to consider the relation between the magnitudes of the magnetic moment /xj and the mechanical angular momentum J. This relation is, in its turn, determined by the Lande factor (the 5-factor), gj see (4.1). 

PROBLEMS AND SOLUTIONS IN QUANTUM CHEMISTRY AND PHYSICS, Charles S. Johnson, Jr. and Lee G. Pedersen. Unusually varied problems, detailed solutions in coverage of quantum mechanics, wave mechanics, angular momentum, molecular spectroscopy, scattering theory, more. 280 problems plus 139 supplementary exercises. 430pp. 6)4 x 4W. 65236-X Pa. 10.95... 

A basic reason for existence of the above-stated problem is that the parameters cited are linked to quantum-mechanical angular-momentum (spin) operators, for instance via the usual spin-Hamiltonian operator... 

Bohr s theory leaves some questions unexplained. Why must the pendulum orbits be excluded The reason given, which points to the collision with the nuchius, is hardly cogent moreover, it is outside the bounds of Bohr s theory. How does the anomalous Zeeman effect come about The explanation of this, as we shall see (p. 140), requires us to use the fact that the el( ctron possesses in itself mechanical angular momentum and magnetic moment. Finally, the calculation of the simplest problem of the type involving more than one body, viz. the lielium problem, h .ads to difficulties, and to results contrary to exjKvrimental facts. 

An important property of quantum-mechanical angular momentum is the prediction and demonstration that the Cartesian components thereof do not commute. This property is responsible for the fact that two components, such as and... 

The helium atom has a metastable Si excited state with quantum numbers a = y a = 1 and a radiative lifetime of 8000 s. To carry out quantum scattering calculations on collisions of two such atoms, we need channel functions to handle the two spin quantum numbers and the mechanical angular momentum L. Once again it would be possible to use simple product functions as channel functions. 

Because the operators 9/S0 are proportional to the quantum mechanical angular momentum operators, the matrix elements Hj (m,m ) are well known (they play an important role in determining the energy levels of a freely rotating asymmetric top). One finds that... 

The micellar structures, lamellar phases, and vesicles formed by fluorinated surfactants and polymers have been investigated by electron spin resonance (ESR) [40-51] (see Section 9.8). Because the micellar systems do not have a net quantum mechanical angular momentum, a paramagnetic probe must be included in the sample (see Section 9.8 for structures of the probes). The use of spin probes is a useful technique for studying micellar systems provided that the probe does not perturb the aggregates being studied. 

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