# I Descriptiveness of this term

1. Mar 10, 2016

### Anton Alice

If you want to modify the Hamiltonian by introducing the effect of an electromagnetic field, then the replacement $$\vec p \rightarrow \vec p - \frac{e}{c}\vec A$$ is applied.

Now my question is, whether there is a descriptive meaning of that extra term $- \frac{e}{c}\vec A$. As what can I think of that?

Last edited: Mar 10, 2016
2. Mar 10, 2016

### say_cheese

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.

3. Mar 11, 2016

### Anton Alice

If small type p is the kinetic momentum, what then is capital P?

4. Mar 11, 2016

### Staff: Mentor

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