Seminarium Fizyki Politechniki Wrocławskiej
PWr, bud. A1, sala 322
Operator Mechanics: A New Form of Quantum Mechanics without Waves or Matrices
Prof. James Freericks
Department of Physics, Georgetown University, United States
Abstract:
Quantum mechanics was created with the matrix mechanics of Heisenberg, Born, and Jordan. Schroedinger’s wave mechanics shortly followed and allowed for simpler and more powerful calculations. Both Pauli and Dirac introduced a formulation of quantum mechanics based on operators and commutation relations, but it was never fully developed in the 1920’s. Instead, Schroedinger formulated the operator approach with his factorization method in 1940, which was adopted by the high-energy community as supersymmetric quantum mechanics in the 1980s.
In this talk, I will explain how one can formulate nearly all of quantum mechanics algebraically by a proper use of the translation operator on top of Schroedinger’s factorization method. I will give examples of how one can compute spherical harmonics algebraically, how one can find harmonic oscillator wavefunctions algebraically, and will even describe an operator-based derivation of the energy eigenstates of Hydrogen. This approach is a representation-independent way to do quantum mechanics. I will end with a description of a novel way to teach quantum mechanics, focusing first on conceptual ideas related to superposition, projective measurements, complementarity, and entanglement. Then developing more conventional topics like spin, harmonic oscillator, angular momentum, central potentials, LIGO and so on. Such a course inevitably focuses much more on the experiments of quantum mechanics, which are often neglected, or given short shrift in conventional treatments. It is most relevant for preparing students for the sensing side of quantum information science. This is how we currently teach quantum mechanics at Georgetown University and a MOOC that covers this material is also available on edX.
Bio:
James Freericks is passionate about making quantum mechanics education more widely accessible so that we can prepare more students for the second quantum revolution. Educated at Princeton University (1985) and the University of California, Berkeley (1987,1991), he held postdoctoral fellowships at the ITP in Santa Barbara and at UC Davis before moving to Georgetown University in 1994. He is a fellow of AAAS and APS and has won awards from the Alpha Sigma Nu Society, the Office of Naval Research, edX, and Georgetown University. He is currently Professor and McDevitt Chair at Georgetown University in the Department of Physics.
