Here, the physical interpretation is of many bosons that interact weakly both with the quantized electromagnetic field (coupling of order 1 N) and among themselves (pair coupling of order 1 N). Defining N 1 / 2 a N − 1 ( k, λ ) and N 1 / 2 a N − 1 * ( k, λ ) as new creation and annihilation operators leads to the mathematically equivalent but physically different choice N → ∞, ℏ = 1, μ N, ℏ = 1 N, and g N = 1 N. At the same time, the coupling between the particles and field is of order one, while the coupling between pairs of particles becomes weak (of order 1 N). In this regime, the electromagnetic field becomes classical inverse proportionally to the increasing number of bosons. 1984 American Association of Physics Teachers. Topics Dirac equation, Schrodinger equations, Dirac particles This content is only available via PDF. The wave function solution for a free particle with U (x) 0 can be. For one spatial dimension, the time-dependent Schrodinger equation takes the form. A possible choice is given by N → ∞, ℏ = 1 N, μ N, ℏ = 1, and g N = 1 N. Finally, the general form for the PauliSchrdinger equation is derived for any 3space orthogonal curvilinear system of coordinates. There is a time-dependent equation for describing progressive waves, which is applicable to free particle motion. This is true only if we couple the parameters N, ℏ suitably and choose the coupling constants μ N, ℏ, g N accordingly. Our aim is to prove that the Maxwell–Schrödinger system emerges in some limit N → ∞ and/or ℏ → 0 as an effective model of the microscopic Pauli–Fierz dynamics.
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