Schrödinger, Heisenberg, and interaction pictures with time dependent Hamiltonians

Next: Quantum mechanics, classical limit   Up: Introduction science education project   Previous: Hong-Ou-Mandel experiment and Bohm

Dated: 01 January 2018

Since the equivalence of the interaction picture with either the Schrödinger or Heisenberg picture was doubted for the time-dependent case (by Daniel Baldomir, if I recall correctly), I here describe the mathematics for all three pictures in a time-dependent setting, which makes the Schrödinger and Heisenberg picture Hamiltonians different. I introduce time-ordered exponentials as needed and this in itself is a fun subject. The equivalence of all three pictures is demonstrated. No attempt at mathematical rigor is made. For example, equations (28a) and (28b) are correct but their "derivation" is sloppy, to say the least. Still, this is a useful piece of education, I believe, and it has reverberations in the interpretational domain.

Schrödinger, Heisenberg, and interaction pictures with time dependent Hamiltonians, 01.01.2018

Next: Quantum mechanics, classical limit   Up: Introduction science education project    Previous: Hong-Ou-Mandel experiment and Bohm

Datenschutzerklärung der Otto-von-Guericke-Universität Magdeburg nach DSGVO