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Any discussion of dynamics and probability must include a discussion of quantum mechanics where dynamics and probability are intertwined in a peculiar way. This chapter cannot, of course, cover quantum mechanics in any substantial way. Instead, we just present with a broad brush the pragmatic rules and some foundational issues of quantum mechanics. Practitioners of quantum mechanics generally agree on the pragmatic rules but disagree on many of the foundational issues. Probability is intrinsic to quantum mechanics. Pure states only have a probabilistic interpretation which derives from a generalization of the Pythagorean theorem rather than from a probability measure. The broadened states of classical mechanics correspond to mixed states in quantum mechanics. There is an additional type of state in quantum mechanics, an entangled state, which does not have any equivalent in classical mechanics. Entangled states derive from the fact that the state space of a composite system is given by the tensor product of the subsystems rather than by the Cartesian product as in classical physics. In quantum mechanics, identical particles are also indistinguishable which led to the non-intuitive counting rules in the chapter on equilibrium statistical mechanics. The differences between quantum and classical mechanics become most succinct when considering the logic applied to propositions in both fields.
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Zurück zum Zitat Alicki, R., Fannes, M.: Quantum dynamical systems. Oxford University Press (2001) Alicki, R., Fannes, M.: Quantum dynamical systems. Oxford University Press (2001)
Zurück zum Zitat Isham, C.J.: Lectures on Quantum Theory. Mathematical and Structural Foundations. Imperial College Press, London (1995) Isham, C.J.: Lectures on Quantum Theory. Mathematical and Structural Foundations. Imperial College Press, London (1995)
- Quantum Mechanics
- Chapter 20