Overview of Quantum Mechanics 1#

Instructors#

  • Lecturer: Dick Furnstahl

Objectives#

Physics 7501 is the first semester of a “Spins First” treatment of quantum mechanics for graduate students at the Ohio State University. See the Bibliography for pointers to texts referenced in the course. This Jupyter Book is being built with Python notebooks to help visualize, explore, and extend the classroom content. Some are original with the instructors but many are borrowed from generous colleagues who have made them freely and publicly available.

The following topics are planned to be covered in 7501, as time permits (the list is not exclusive of other topics):

  • Linear vector spaces, operators, eigenvalue problems

  • Why quantum mechanics is needed; quantum mechanical postulates

  • Measurements, observables, uncertainty relations

  • Change of basis; position, momentum, translation

  • Time evolution; Schrodinger vs. Heisenberg picture

  • The harmonic oscillator

  • Representative problems in one dimension

  • First pass at path integral formulation of quantum theory; the classical limit

  • Symmetries and conservation laws in quantum mechanics

  • Rotational symmetry and angular momentum; spin; three-dimensional problems

  • Introduction to approximation methods; computational methods

  • Special topics: entanglement, Bell’s theorem, quantum computing