2. Introduction to Quantum Mechanics 2.1 Laws of Quantum Mechanics 2.2 States, Observables and Eigenvalues 2.2.1 Properties of Eigenfunctions 2.2.2 Review of Linear Algebra 2.3 Measurement and Probability 2.3.1 Wavefunction Collapse 2.3.2 Position Measurement 2.3.3 Momentum Measurement 2.3.4 Expecta

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Abstract	Every physical theory is formulated in terms of mathematical objects. It is thus necessary to establish a set of rules to map physical concepts and objects into mathematical objects that we use to represent them. Sometimes this mapping is evident, as in classical mechanics, while for other theories, such as quantum mechanics, the mathematical objects are not intuitive. In the same way as classical mechanics is founded on Newton's laws or electrodynamics on the Maxwell-Boltzmann equations, quantum mechanics is also based on some fundamental laws, which are called the postulates or axioms of quantum mechanics. We want in particular to develop a mathematical model for the dynamics of closed quantum systems 1 : therefore we are interested in defining states – observables – measurements – evolution Some subtleties will arise since we are trying to define measurement in a closed system, when the measuring person is instead outside the system itself. A more complete picture, that can explain some of the confusion arising from the measurement process, is possible, but we will not study it in this course. We are interested in giving a description of physical phenomena and in particular in how they emerge during an experiment. Experiments – A physical experiment can be divided into two steps: preparation and measurement. In classical mechanics (CM):-the first step determines the possible outcomes of the experiment,-while the measurement retrieves the value of the outcome. In quantum mechanics (QM) the situation is slightly different:-the first step (preparation) determines the probabilities of the various possible outcomes,-the second step (measurement) retrieve the value of a particular outcome, in a statistic manner. This separation of the experiment in two steps is reflected into the two types of operators that we find in QM.-The first step corresponds to the concept of a state of the system, 1 We define a closed system any system that is isolated, thus not exchanging any input or output and not interacting with any other system. An open system instead interacts e.g., with an external environment.
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Alternate Webpage(s)	http://ocw.mit.edu/courses/nuclear-engineering/22-02-introduction-to-applied-nuclear-physics-spring-2012/lecture-notes/MIT22_02S12_lec_ch2.pdf
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