Mathematical Primer on Quantum Mechanics

Alessandro Teta is an Associate Professor in the Department of Mathematics “G. Castelnuovo”, University of Rome "La Sapienza", Rome, Italy. He graduated in Physics from the University of Napoli in 1985 and then completed a PhD in Mathematical Physics at S.I.S.S.A. Trieste. In 1992 he was appointed Researcher in Mathematical Physics at University of Roma "La Sapienza" and in 1999 became Associate Professor in Mathematical Physics at Universita' di L'Aquila. In 2013 he completed his Habilitation to full professor in Mathematical Physics. Dr. Teta’s research interests include the effective behavior of inhomogeneous media and mathematical problems in quantum mechanics: scattering theory, spectral analysis, Schroedinger operators with zero-range interactions, nonlinear Schroedinger equations, effective equations for systems of infinite quantum particles, the classical limit, decoherence, and models of cloud chamber. Dr. Teta is a member of the International Association of Mathematical Physics and the International Research Center on Mathematics and Mechanics of Complex Systems. He has presented numerous invited talks at conferences in Italy and across Europe.

“The presentation is well-structured and easy to follow, with ample examples and exercises. It can hence be used both as a basis for a course on this topic as well as for self study. It is a welcome addition to the textbook literature on this subject.” (G. Teschl, Monatshefte für Mathematik, Vol. 191 (3), 2020)“This book fills the gap between the elementary classical and quantum mechanics … and higher-level mathematics required to study more advanced books. Indeed, after reading this Primer a student would have enough motivation and basic understanding of the theory of (un)bounded linear operators to read … .I highly recommend it especially for physics students, who after reading this Primer should be fully prepared and motivated to study a more advanced references … .” (Arsen Melikyan, zbMATH 1394.81006, 2018)

• Preface.- 1. Brief Review of Hamiltonian Mechanics and Electromagnetism.- 2. From Planck's Hypothesis to Bohr's Atom.- 3. Schrodinger Equation.- 4. Linear Operators in Hilbert Spaces.- 5. Rules of Quantum Mechanics.- 6. Free Particle.- 7. Harmonic Oscillator.- 8. Point Interaction.- 9. Hydrogen Atom.- 10. The Cloud Chamber Problem.- References.- Index.