## Foundations of Quantum Mechanics II (Texts and Monographs in by Gunther Ludwig

By Gunther Ludwig

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Heisenberg's own exposition (Heisenberg 1930) and Feynman's introduction (Feynman et 1965) are particularly recommended. al. Problems on Chapter 1 1. In electrolysis metal ions in solution are attracted to a negatively charged plate (the cathode). 65 x 107 coulomb kg - 1 if I is measured in coulombs per second. Calculate Avogadro's number (the number of atoms of atomic weight A in a mass of A kg). 2. Calculate the mass of the electron in kg. [A charge of 1 coulomb falling through a potential difference of 1 volt acquires energy of 1 joule.

In each case there is a mathematical object which describes the state of the properties we . are interested in: the state of an electron as far as its position is concerned (ignoring any other properties it may have) is described by the wave function l/J(r), while the state of polarisation of a photon (ignoring its position, and assuming it has a particular direction of motion) is described by the polarisation vector t/I. ) The objects tfr(r) and t/l are very different mathematically (as one might expect, position and polarisation being very 44 2 Quantum statics different physical properties), but they share certain features which must be present in the description of any quantum system.

Nuclear forces. 24(a). I I I t i I I Fig. 23. Nuclear forces at the quark level. 'Tr 1 34 Particles and forces of the electromagnetic force on a particle is determined by its electric charge. Now gluons must also be regarded as coloured (since they carry colour from one quark to another), and so they themselves experience the same force as quarks. This means that there is a three-gluon vertex, Fig. 24(b). There is also a four-gluon vertex, Fig. like the four-W vertex in the electroweak force: the theory of the interquark force is also a non-abelian gauge theory.