Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

by equivalent I mean:

  1. the Hilbert spaces are isomorphic;
  2. the operators can therefore be mapped 1:1
share|cite|improve this question

If the Hamiltonian commutes with the particle number operator then no particles are created or destroyed. In that case you can restrict the Fock space to the sector with a specified number of particles (e.g., all states with $N$ particles). The second quantized theory on this sector of Fock space is isomorphic to the first quantized theory described by the many-body wavefunction $\Psi(r_1, r_2,\ldots,r_N)$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.