Classical Angular Momentum

In the configuration space spanned by (411,1 2, 73), we may then define the vibrational angular momentum k through its classical components, that is,... 

In the classical picture of an electron orbiting round the nucleus it would not surprise us to discover that the electron and the nucleus could each spin on its own axis, just like the earth and the moon, and that each has an angular momentum associated with spinning. Unfortunately, although quantum mechanical treatment gives rise to two new angular momenta, one associated with the electron and one with the nucleus, this simple physical... 

The quantum generalization of the APR Hamiltonian results after supplementing this classical Hamiltonian with a non-commuting angular momentum part [Lj, p] = -ihSji which introduces quantum dispersion and thus qualitatively new effects due to additional fluctuations and tunnehng. 

Consider a nucleus with magnetic moment pi in a magnetic field Ho- According to classical mechanics the rate of change of the angular momentum G is the torque T. 

The Stern-Gerlach experiment demonstrated that electrons have an intrinsic angular momentum in addition to their orbital angular momentum, and the unfortunate term electron spin was coined to describe this pure quantum-mechanical phenomenon. Many nuclei also possess an internal angular momentum, referred to as nuclear spin. As in classical mechanics, there is a relationship between the angular momentum and the magnetic moment. For electrons, we write... 

The quasi-classical theory of spectral shape is justified for sufficiently high pressures, when the rotational structure is not resolved. For isotropic Raman spectra the corresponding criterion is given by inequality (3.2). At lower pressures the well-resolved rotational components are related to the quantum number j of quantized angular momentum. At very low pressure each of the components may be considered separately and its broadening is qualitatively the same as of any other isolated line in molecular or atomic spectroscopy. 

Our calculations have been successful in interpreting trends that are seen in the experimentally observed rates of electron ejection. However, until now, we have not had a clear physical picture of the energy and momentum (or angular momentum) balancing events that accompany such non BO processes. It is the purpose of this paper to enhance our understanding of these events by recasting the rate equations in ways that are more classical in nature (and hence hopefully more physically clear). This is done by... 

Remarkably, only one nuclear constant, Q, is needed in (4.17) to describe the quadrupole moment of the nucleus, whereas the full quadrupole tensor Q has five independent invariants. The simplification is possible because the nucleus has a definite angular momentum (7) which, in classical terms, imposes cylindrical symmetry of the charge distribution. Choosing x, = z as symmetry axis, the off-diagonal elements Qij are zero and the energy change caused by nuclear... 

Angular momentum plays an important role in both classical and quantum mechanics. In isolated classical systems the total angular momentum is a constant of motion. In quantum systems the angular momentum is important in studies of atomic, molecular, and nuclear structure and spectra and in studies of spin in elementary particles and in magnetism. 

We first consider a particle of mass m moving according to the laws of classical mechanics. The angular momentum L of the particle with respect to the origin of the coordinate system is defined by the relation... 

The quantum-mechanical operators for the components of the orbital angular momentum are obtained by replacing px, Py, Pz in the classical expressions (5.2) by their corresponding quantum operators. 

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