Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Second Quantization

  1. Dec 1, 2011 #1
    Hi,all
    What is the motivation of using Second Quantization ?
    What kind of situation does people want to use field operators ?
    Euphemia
     
  2. jcsd
  3. Dec 1, 2011 #2

    atyy

    User Avatar
    Science Advisor

    In non-relativistic quantum mechanics, second quantization is mathematically equivalent to the Schroedinger equation. Take a lattice of atoms and write the Schroedinger equation. Second quantization essentially just taking the Fourier transform, and the "particles" are Fourier modes. Since it is natural for Fourier modes to be created and destroyed, these are useful for describing "particles" which are created and destroyed. In the relativistic case, one postulates the second quantized version directly without an underlying lattice.
     
  4. Dec 1, 2011 #3

    tom.stoer

    User Avatar
    Science Advisor

    The framework of non-rel. QM based on the Schroedinger equation is not suitabe for the description of creation and annihilation of particles, e.g. electron - positron annihilation (and production of two photons). In order to achieve that one needs 'second quantization'
     
  5. Dec 2, 2011 #4

    Demystifier

    User Avatar
    Science Advisor

    In non-relativistic QM, second quantization is a mathematical trick useful to write many-particle wave functions in a symmetric (Bose-Einstein statistics) or antisymmetric (Fermi-Dirac statistic) form automatically.
     
  6. Dec 2, 2011 #5

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    There's no <second> quantization, there's only <quantization> which means passing from classical Hamiltonian observables to quantum counterparts where they exist and are uniquely defined (Groeneveld-van Hove problem).
     
  7. Dec 2, 2011 #6

    qsa

    User Avatar

  8. Dec 2, 2011 #7
    Calculating Occupation Numbers. It's a math trick at best.
     
  9. Dec 2, 2011 #8

    Fra

    User Avatar

    Meaning you can either see it as a one time thing (and then face the question, why stop there?), or (the way I prefer it) as defining an induction step and then worry about howto interpret that tower of turtles.

    http://math.ucr.edu/home/baez/nth_quantization.html contains some interesting ponderings.

    /Fredrik
     
  10. Dec 2, 2011 #9

    A. Neumaier

    User Avatar
    Science Advisor
    2016 Award

    It is very basic for an understanding of quantum statistical mechanics, where almost everything gets much simpler in the second quantization formulation using fields.

    Some people don't like the terminology, but it is very standard.
    (But one should not imagine that it is literally a quantization of something already quantized.)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Second Quantization
  1. Second quantization (Replies: 8)

  2. Second Quantization (Replies: 4)

  3. Second quantization (Replies: 6)

  4. Second Quantization (Replies: 1)

  5. Second quantization (Replies: 9)

Loading...