Syllabus
* Standard quantum mechanics (QM).
Arrival of the quantum world on stage. Nature of the quantum description. Quantum states and measurement process. Specification of a quantum system. Statistical description. Time evolution. Compound systems. Quantum measurement and nature of state reduction. Interpretations of QM and their problems.
* Theory of hidden variables.
Motivation. Arguments against hidden-variable theories. Bell inequalities.
* Measurement theory.
Measurement of location by means of immediate interaction. Measurements of momentum and of more complicated observables. Stern-Gerlach experiment. Decoherence and effective reduction.
* Everett interpretation of QM.
QM without state reduction. Quantitative predictions. One observer. Two observers. Tunneling between branches.
* Feynman formulation of QM.
Histories and systems of histories. Quantum indistinguishability. Structure of histories. Amplitude and probability rules. Slit scatterings. Feynman integral. Symmetries and indistinguishable particles. Relation to standard QM.
* Generalised QM.
Wigner formula. Interference and decoherence. Consistence of histories. Decoherence functional and decohering histories.
* Interesting points.
Quantum cryptography. Quantum teleportation. Quantum bomb testing. Quantum cosmology.
Annotation
The course will concentrate on the foundations of quantum mechanics, especially on quantum measurement. We will discuss various interpretations of QM, their relations, advantages, and problems.
Standard quantum mechanics. Reality and localization of the state collapse. Decoherence. Theory of hidden variables. Theory of measurement. Everett interpretation. Feynman formulation. Generalized QM.
Lectures complementary to the standard course of QM. No deeper knowledge of QM is assumed.