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Physics Colloquium: James Freericks (Georgetown University)

September 28 | 4:00 pm - 5:00 pm

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Title: Operator Mechanics: A new form of quantum mechanics without
waves or matrices

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, which later was adopted by the
high-energy community as supersymmetric quantum mechanics. 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, and will even describe an
operator-based derivation of the wavefunctions of Hydrogen. I will end
with a proposal for a novel way to teach quantum mechanics, focusing
first on conceptual ideas related to superposition, projective
measurements, and entanglement. Then developing more conventional
topics like spin, harmonic oscillator, angular momentum, interacting
spin models, central potentials, particles in a box and so on. This is
the subject of a book in progress entitled Quantum Mechanics without

Host: Lex Kemper



September 28

4:00 pm - 5:00 pm
Event Category: