By A. R. Edmonds
This booklet bargains a concise advent to the angular momentum, probably the most basic amounts in all of quantum mechanics. starting with the quantization of angular momentum, spin angular momentum, and the orbital angular momentum, the writer is going directly to talk about the Clebsch-Gordan coefficients for a two-component process. After constructing the mandatory arithmetic, particularly round tensors and tensor operators, the writer then investigates the 3-j, 6-j, and 9-j symbols. all through, the writer presents functional functions to atomic, molecular, and nuclear physics. those comprise partial-wave expansions, the emission and absorption of debris, the proton and electron quadrupole second, matrix aspect calculation in perform, and the houses of the symmetrical best molecule.
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Extra info for Angular momentum in quantum mechanics
108) deduced from this that the atom should consist of a heavy central mass, concentrated within a very small volume, surrounded by light masses of opposite charge, occupying the outer parts of the atom. We shall briefly discuss the considerations which led Rutherford to this conclusion. In the light of m o d e m nuclear physics and elementary physics experiments, it is interesting to note that Rutherford emphasizes the importance of scattering experiments involving high-energy particles for the study of atomic structure.
Scattering in the centre of mass and laboratory systems. We note that if m<^M, « 0,^, as we would have expected. If /n = Af, we see that although θ^^ and θ^^ differ, the scattering angle in the laboratory system can still vary from 0 to π just as the scattering angle in the centre of mass system. However, if mt> M,y/e see that although the scattering angle in the centre of mass system can become large, in the laboratory system the scattering angle will always be small. In the Thomson atom, the scattering is due to the corpuscles (electrons), while in the Rutherford atom, it is partly due to the electrons and partly due to the nucleus.
Lnpdp. If η is the number of scattering nuclei per unit volume and t the thickness of the target, and A its area at right angles to the incident beam, the number dN of particles scattered through angles between θ^^ and θ^ο + αθ^^ will be dN =; lAtnlnpdp = ^nlAtnb^^^^^de,,. 9) the differential cross-section άσ ^ = IAt. 2π sin 0sc d9sc and we have the so-called Rutherford scattering formula. 11) and we see that/decreases rapidly with increasing θ^^. This means that the average scattering angle < 0 s c > will be small.
Angular momentum in quantum mechanics by A. R. Edmonds