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I Descriptiveness of this term

  1. Mar 10, 2016 #1
    If you want to modify the Hamiltonian by introducing the effect of an electromagnetic field, then the replacement [tex]\vec p \rightarrow \vec p - \frac{e}{c}\vec A [/tex] is applied.

    Now my question is, whether there is a descriptive meaning of that extra term [itex]- \frac{e}{c}\vec A[/itex]. As what can I think of that?
    Thank you in advance
    Last edited: Mar 10, 2016
  2. jcsd
  3. Mar 10, 2016 #2
    One way to look at it is that it is the momentum imparted through the electromagnetic force,

    Momentum wikipedia -
    The classical Hamiltonian ℋ for a particle in any field equals the total energy of the system – the kinetic energy T = p2/2m (where p2 = p · p, see dot product) plus the potential energy V. For a particle in an electromagnetic field, the potential energy is V = , and since the kinetic energy T always corresponds to the kinetic momentum p, replacing the kinetic momentum by the above equation (p = PqA) leads to the Hamiltonian in the table.
  4. Mar 11, 2016 #3
    If small type p is the kinetic momentum, what then is capital P?
  5. Mar 11, 2016 #4


    User Avatar

    Staff: Mentor

    It's the canonical momentum, i.e., the total momentum of the particle.
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