Titlebook: Lectures on the Mathematics of Quantum Mechanics II: Selected Topics; Gianfausto Dell‘Antonio Book 2016 Atlantis Press and the author(s) 2

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Lecture 13: The N-Body Quantum System: Spectral Structure and Scattering,complete analysis and further references we refer to W. Hunziker, I. Sigal, Am. Math. Soc. 8:35–72, 1995, [.], M. Reed, B. Simon, Methods of Modern Mathematical Physics, 1978, [.], W. Hunziker, I.M. Sigal, J. Math. Phys. 41:3448–3510, 2000, [.], R.G. Froese, I. Herbst, Duke Math. J. 49:1075–1085, 1982, [.].

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https://doi.org/10.2991/978-94-6239-115-4Lecture notes; Mathematics of Quantum Mechanics; Quantum Mechanics; Quantum Physics; Selected Topics in

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Lecture 1: Wigner Functions. Coherent States. Gabor Transform. Semiclassical Correlation Functions,In Classical Mechanics a pure state is described by a Dirac measure supported by a point in phase space.

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,Lecture 4: Periodic Potentials. Wigner–Seitz Cell and Brillouen Zone. Bloch and Wannier Functions,In this lecture we will give some basic elements of the theory of Schroedinger equation with periodic potentials.

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,Lecture 6: Lie–Trotter Formula, Wiener Process, Feynman–Kac Formula,We begin recalling the Lie–Trotter formula.

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Lecture 7: Elements of Probability Theory. Construction of Brownian Motion. Diffusions,We return briefly in this lecture to the realization of the Wiener process; we study here its realization from the point of view of semigroup theory, using transition functions. The same approach will be used in the next lecture to study the Ornstein–Uhlenbeck process.