Gauge invariant hydrogen atom Hamiltonian

Details Gauge invariant hydrogen atom Hamiltonian Gauge invariant hydrogen atom Hamiltonian

2010-02-18

arxiv.org/abs/1002.3421v3

Phys. Rev. A 82, 012107 (2010)

Physics

High Energy Physics

High Energy Physics - Phenomenology

7 pages, revtex4, some further discussion on Dirac Hamiltonian and the gauge invariant Hamiltonian is added, one reference rem

Scientific paper

For quantum mechanics of a charged particle in a classical external electromagnetic field, there is an apparent puzzle that the matrix element of the canonical momentum and Hamiltonian operators is gauge dependent. A resolution to this puzzle is recently provided by us in [2]. Based on the separation of the electromagnetic potential into pure gauge and gauge invariant parts, we have proposed a new set of momentum and Hamiltonian operators which satisfy both the requirement of gauge invariance and the relevant commutation relations. In this paper we report a check for the case of the hydrogen atom problem: Starting from the Hamiltonian of the coupled electron, proton and electromagnetic field, under the infinite proton mass approximation, we derive the gauge invariant hydrogen atom Hamiltonian and verify explicitly that this Hamiltonian is different from the Dirac Hamiltonian, which is the time translation generator of the system. The gauge invariant Hamiltonian is the energy operator, whose eigenvalue is the energy of the hydrogen atom. It is generally time-dependent. In this case, one can solve the energy eigenvalue equation at any specific instant of time. It is shown that the energy eigenvalues are gauge independent, and by suitably choosing the phase factor of the time-dependent eigenfunction, one can ensure that the time-dependent eigenfunction satisfies the Dirac equation.

Affiliated with

Also associated with

No associations

Rating

Gauge invariant hydrogen atom Hamiltonian does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Gauge invariant hydrogen atom Hamiltonian, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Gauge invariant hydrogen atom Hamiltonian will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-404616