Discussion Overview
The discussion revolves around the interaction Hamiltonian between an electron in an atom and an electromagnetic wave, particularly focusing on the presence of a factor of 2 in the Hamiltonian expressions. Participants explore the implications of different formulations of the Hamiltonian and their relation to classical and quantum descriptions of electromagnetic fields.
Discussion Character
- Technical explanation
- Debate/contested
- Conceptual clarification
Main Points Raised
- One participant presents two forms of the interaction Hamiltonian, questioning which is correct: H_{int} = \vec{E_0} \vec{r} \cos(\omega t) or H_{int} = 2 \vec{E_0} \vec{r} \cos(\omega t).
- Another participant suggests that the choice of field representation is a matter of convention and emphasizes the importance of consistency in the chosen conventions.
- A different participant challenges the idea that it is merely a convention, asserting that the amplitude of the field should be E, not 2E.
- One participant notes that the dipole moment operator is defined as E.r, indicating that the factor of 2 must arise from the field's definition.
- Another participant mentions that the factor of 2 may stem from the quantum nature of the electromagnetic field and suggests that including it is necessary for obtaining correct classical results.
- A later post introduces a coupling assumption using the electromagnetic field operator in quantum electrodynamics (QED) and questions whether a classical result can be recovered under this framework.
Areas of Agreement / Disagreement
Participants express differing views on whether the factor of 2 is a matter of convention or a necessary component for accurate calculations. The discussion remains unresolved with multiple competing perspectives on the correct formulation of the interaction Hamiltonian.
Contextual Notes
There are unresolved assumptions regarding the definitions of the electromagnetic field and the implications of quantum versus classical treatments. The discussion does not clarify the specific contexts in which each formulation may be applicable.