Particles moving in one dimension and their operators

Quantum Mechanics (Winter, 2012)

February 27, 2012

Professor Susskind opens the lecture by examining entanglement and density matrices in more detail.  He shows that no action on one part of an entangled system can affect the statistics of the other part.  This is the principle of locality and is directly connected to the requirement that systems evolve over time only through unitary operators.  Violating locality implies non-local hidden variables which are equivalent to wires that transmit information instantaneously.  These would allow true "spooky action at a distance," but they don't exist.

Professor Susskind then discusses the simplest possible continuous system of a particle moving in one dimension.  He presents the wave function for such a system, and discusses its Hermitian operators and observables including the operators corresponding to position, momentum, and energy.  The energy operator is the Hamiltonian, and generates the time evolution of a system.  Finally, he presents the difference between the Hamiltonian for a relativistic particle moving with a constant velocity in any reference frame (e.g. a photon or neutrino), and a non-relativistic particle (i.e. one with mass).

  • Is entanglement reversible?
  • Continuous systems
  • A particle moving in one dimension
  • Position, momentum, and energy operators
  • Hamiltonian operator generates the time evolution of a system