Abstract
The structure of quantum systems is studied by “looking at them” with light or with other quantum systems such as electrons that are usually more fundamental and have less structure than the physical system being investigated. If a quantum particle has no internal structure and is a point object, it is fundamental and is called an elementary particle.
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Notes
- 1.
See A. Bohm, Quantum Mechanics: Foundations and Applications 3rd Ed. Springer, New York, 2008, eq. (7.50).
- 2.
For example, when U(Q 2 −Q 1) = k[(Q 2 −Q 1)2] = k[(Q 2)2 + (Q 1)2 + 2Q 1 Q 2], the final term prevents U from being written as the direct product U = U 1 ⊗ 1 + 1 ⊗ U 2.
- 3.
In molecular physics wave number is expressed in cm−1 and is denoted by ν, a convention followed here.
- 4.
Mathematically this assumption can be stated: the conditions of the nuclear spectral theorem are fulfilled.
- 5.
A. Bohm, The Rigged Hilbert Space and Quantum Mechanics, Lecture Notes in Physics, 78 (1978), Springer-Verlag, Berlin, Heidelberg, New York.
- 6.
For example, the group G could be the rotation group SO(3) describing an elementary rotator and \(\mathcal {E}(SO(3))\) is the algebra generated by the angular momentum operators J i discussed in Chap. 2, Sect. 2.3. Or if G is the group E(3), then \(\mathcal {E}(G)\) is the algebra generated by the momentum operators J i and the position operators Q i describing the rotating dumbbell of Chap. 2, Sect. 2.4.
- 7.
As is customary in the literature on molecular spectra, frequencies have been converted to wave-number units by dividing by a factor of c (in cm/s), resulting in frequencies measured in cm−1.
- 8.
Note that the same symbol ν is used for the frequency (in s−1) and the wave number (in cm−1).
- 9.
ω e ξ e is given by the anharmonicity of the oscillator (terms proportional to Q 3, Q 4, etc.) and can be calculated by perturbation theory.
- 10.
For an orbital angular momentum ℓ = 2 component of the deuteron see H. Frauenfelder and E. M. Henley, Subatomic Physics, Sect. 14.5, Prentice Hall (1991).
- 11.
M.E. Rose, Elementary Theory of Angular Momentum (New York: John Wiley, 1957).
- 12.
A. R. Edmonds, Angular Momentum in Quantum Mechanics. Princeton University Press, Princeton, 1957.
- 13.
Ibid, pp. 44, 45.
- 14.
Here only “irreducible tensor operators” are considered.
- 15.
In labeling the components of vector operators, spherical components are denoted by Greek letters and Cartesian components by Latin letters. This notation is not used for the general tensor operator.
- 16.
In some textbooks, a constant factor or function of j appears explicitly in the Wigner-Eckart theorem. In the notation used here these factors have been absorbed into the reduced matrix element.
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Bohm, A., Kielanowski, P., Mainland, G.B. (2019). Combinations of Quantum Physical Systems. In: Quantum Physics. Springer, Dordrecht. https://doi.org/10.1007/978-94-024-1760-9_3
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