Physics Colloquium: A New Form of Quantum Mechanics without Waves or Matrices

Physics Colloquium
Operator Mechanics: A New Form of Quantum Mechanics without Waves or Matrices

Dr. James Freericks
Professor of Physics and McDevitt Chair
Georgetown University

Such a course inevitably focuses much more on the experiments of quantum mechanics, which are often neglected, or given short shrift in conventional treatments.

Abstract:
Quantum mechanics was created with the matrix mechanics of Heisenberg, Born, and Jordan. Schrödinger’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, Schrödinger formulated the operator approach with his factorization method in 1940, which later 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 Schrödinger’s factorization method. I will give examples of how one can compute spherical harmonics algebraically, how one can find harmonic oscillator wavefunctions, and will even describe an operator-based derivation of the wave functions 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. This is the subject of a book in progress entitled Quantum Mechanics without Calculus. More information about this work is available at https://quantum.georgetown.domains

Speaker Bio
James Freericks has a long-standing interest in bringing the ideas of quantum mechanics to the broadest audiences. He has a MOOC entitled Quantum Mechanics for Everyone on edX that has enrolled 45,000 students and is number 7 on the top 250 MOOCs of all time at classcentral. In addition to quantum pedagogy, he works on quantum computing and on the theory behind pump/probe experiments. He is Professor and McDevitt Chair of Physics at Georgetown University, where he has been since 1994. He received his Bachelor's degree from Princeton and his Ph. D. from the University of California, Berkeley. He is a Fellow of the American Physical Society, of the American Association for the Advancement of Science and has won awards from the Office of Naval Research, the Alpha Sigma Nu Society, edX, and Georgetown University.

Intended Audience:
Beginners, undergraduates, graduates, experts. Those with interest in the topic.

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