Quantum mechanics nomenclature

Modem quantum-mechanical Valence-Bond (VB) theory has firm roots back to classical ideas even of a century and a half ago. These connections are of special interest, especially if greater general insight and extension of the classical concepts can be made. The interconnecting simpler semiempirical approaches, such as are of the prime focus here, are historically inextricably mixed with that of the ab initio theory, and the development has been via a peculiarly torturous road toward quantitative relevance. Thence here some brief historical commentary which also sets some nomenclature and ideas is first made. 

In a paper in 1979, Carl Ballhausen [1] expressed the belief that today we realize that the whole of chemistry is one huge manifestation of quantum phenomena, but he was perfectly well aware of the care that had to be taken to express the relevant quantum theory appropriately. So in an earlier review [2] that he had undertaken with Aage Hansen, he scorned the usual habit of chemists in naming an experimental observation as if it was caused by the theory that was used to account for it. Thus in the review they remark that a particular phenomenon observed in molecular vibration spectra is presently refered to as the Duchinsky effect. The effect is, of course, just as fictitious as the Jahn-Teller effect. Their aim in the review was to make a start towards rationalization of the nomenclature and to specify the form of the molecular Hamiltonian implicit in any nomenclature. In an article that Jonathan Tennyson and I published in the festschrift to celebrate his sixtieth birthday in 1987 [3], we tried to present a clear account of a molecular Hamiltonian suitable for treating the vibration rotation spectrum of a triatomic molecule. In an article that I wrote that appeared in 1990 [4], I discussed the difficulty of deciding just how far the basic chemical idea of molecular structure could really be fitted into quantum mechanics. 

Within the Dirac nomenclature of quantum mechanics the state vector is called ket and denoted as xfr). Such a ket is analogous to a wave function but it need not be specified in an explicit form. The ket may often be represented as a column vector (n x 1 matrix). Then the adjoint matrix—a row vector— represents the bra vector denoted as [x(r, i e. 

Quantization as an eigenproblem. Well, once upon a time quantum mechanics was discussed in German. Some traces of that period remain in the nomenclature. One is the eigenvalue problem or e nproblem which is a German-English hybrid. 

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