Quantum Mechanics for Mathematicians
- Formation and generalization of knowledge on quantum mechanics at the level of fundamental physical theory; mastering the mathematical apparatus of quantum mechanics; formation of the ability to apply theoretical knowledge in solving problems of quantum mechanics; the development of physical thinking; mastery of theoretical methods of cognition.
- To have a concept of the algebra of observables and states in classical mechanics. To know Liouville’s theorem, and two pictures of motion in classical mechanics. To understand the physical bases of quantum mechanics.
- To have a concept of the observables and states in quantum mechanics. To know Heisenberg uncertainty relations. Physical meaning of the eigenvalues and eigenvectors of observables. To understand two pictures of motion in quantum mechanics. To be able to write and solve Schrödinger equation. To be able to find stationary states.
- To know the Heisenberg commutation relations. To be able to pass from coordinate representations to momentum representations and back. To have a concept of eigenfunctions of the operators Q and P. To know the interconnection between quantum and classical mechanics. To be able to calculate the eigenfunctions and eigenvalues of the free one-dimensional particle and harmonic oscillator. To have a concept of the angular momentum of a three-dimensional particle.
- Elements of classical mechanics and physical bases of quantum mechanics
- A finite-dimensional model of quantum mechanics
- Quantum mechanics of real systems
- John Archibald Wheeler, & Wojciech Hubert Zurek. (1983). Quantum Theory and Measurement. Princeton University Press.
- Rivers, R. J. (2012). Path Integrals for (Complex) Classical and Quantum Mechanics. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.1202.4117
- S. J. Gustafson, I. M. Sigal, Mathematical Concepts of Quantum Mechanics / Springer-Verlag Berlin Heidelberg 2011
- Simon, Barry. Functional Integration and Quantum Physics / Barry Simon. – Academic Press, 1979
- Alyssa Ney, David Z Albert, & Craig Callender. (n.d.). eds.) (2013): The wave function: essays in the metaphysics of quantum mechanics.
- Neumaier, A., & Westra, D. (2008). Classical and Quantum Mechanics via Lie algebras. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.0810.1019
- Tim Maudlin. (2019). Philosophy of Physics : Quantum Theory. Princeton University Press.
- Zinn-Justin, J. (2010). Path Integrals in Quantum Mechanics. Oxford: OUP Oxford. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=643992