QM

Quantum Mechanics

Objectives

Understands how a beam-splitter and a Mach-Zhender interferometer works Understands the concept of quantum interferences among alternative paths Understands the Stern-Gerlach experiment and its implications Expresses spin 1⁄2 states in Dirac notation and in different basis Understands the concept of Bloch sphere Builds the spin 1⁄2 operators as Pauli matrices Understands the concept of an eigenvalue problem Solves eigenvalue problems Knows the concept of commutator between to operators Builds two-electron states Understands the concept of quantum entanglement Solves the particle in a box problem Solves scattering problem in 1D Solves the harmonic oscillator problem Operates with creation and annihilation operators Knows the solution of problems with spherical symmetry Utilizes the angular momentum operators Uses the spherical harmonics functions in 3D problems Solves the quantum Coulomb problem

Program

• Spin states and Dirac notation.
• Two electrons spin states and entanglement.
• Eigenvalue problems.
• The Hamiltonian and the time evolution of states.
• Bound states in 1D.
• Scattering states in 1D.
• Solution of the quantum harmonic oscillator problem using two different approaches.
• Three-dimensional problems and the angular momentum operators.
• Spherical harmonics.
• Solution of the hydrogen-atom problem.

Bibliography

Pieter Kok, A First Introduction to Quantum Physics, (Springer, 2018) John S. Townsend, A Modern Approach to Quantum Mechanics, (University Science Books, 2012) John S. Townsend, Quantum Physics: A Fundamental Approach to Modern Physics, (University Science Books, 2010)