The quantum mechanics of an oscillator interacting with a field in the limit of zero damping (\ensuremath{\lambda}+0) and infinite field extension (\ensuremath{\Lambda}\ensuremath{\rightarrow}\ensuremath{\infty}) depends on the order in which the limits are taken. If the limit \ensuremath{\lambda}\ensuremath{\rightarrow}0 is taken after the limit \ensuremath{\Lambda}\ensuremath{\rightarrow}\ensuremath{\infty}, one obtains Gaussian wave functions for all stationary states (m=0,1,2,. . .) of the particle. These Gaussians do have the correct standard values for the variances 〈${\ensuremath{\zeta}}^{2}$ ${〉}_{n}$ but otherwise obviously differ from the standard harmonic-oscillator result. The latter arises only if the zero-damping limit is taken before the infinite-system limit.The quantum mechanics of an oscillator interacting with a field in the limit of zero damping (\ensuremath{\lambda}+0) and infinite field extension (\ensuremath{\Lambda}\ensuremath{\rightarrow}\ensuremath{\infty}) depends on the order in which the limits are taken. If the limit \ensuremath{\lambda}\ensuremath{\rightarrow}0 is taken after the limit \ensuremath{\Lambda}\ensuremath{\rightarrow}\ensuremath{\infty}, one obtains Gaussian wave functions for all stationary states (m=0,1,2,. . .) of the particle. These Gaussians do have the correct standard values for the variances 〈${\ensuremath{\zeta}}^{2}$${〉}_{n}$ but otherwise obviously differ from the standard harmonic-oscillator result. The latter arises only if the zero-damping limit is taken before the infinite-system limit.

Physical Review AMar 1, 19865 citations

Quantum Electrodynamics with Infinitesimal Nonlinear Interactions

Kan-ichi Yokoyama

Progress of Theoretical PhysicsFeb 1, 19700 citations

Infinite multilevel system coupled to a quantum-field mode

Markus Lindberg, Erkki Kyrola

We investigate a multilevel system coupled to a quantum-field mode, neglecting the damping. The model is shown to be exactly solvable in the case of equal couplings and detunings. The eigenvalues and eigensolutions are calculated. We compute the time evolution of the level populations. The behavior is compared with that of the corresponding exactly solvable semiclassical model, in which the quantum mode is replaced with an external classical field, and with that of the Maxwell–Bloch model, in which the ladder and field variables are decorrelated in the lowest nontrivial order. The semiclassical limit of the quantum system is also studied.We investigate a multilevel system coupled to a quantum-field mode, neglecting the damping. The model is shown to be exactly solvable in the case of equal couplings and detunings. The eigenvalues and eigensolutions are calculated. We compute the time evolution of the level populations. The behavior is compared with that of the corresponding exactly solvable semiclassical model, in which the quantum mode is replaced with an external classical field, and with that of the Maxwell–Bloch model, in which the ladder and field variables are decorrelated in the lowest nontrivial order. The semiclassical limit of the quantum system is also studied.

Journal of the Optical Society of America BApr 1, 199214 citations

Non-linear effects in quantum electrodynamics

Shane Jerome Kohler

Dec 1, 20101 citation

{〉}_{n}

but otherwise obviously differ from the standard harmonic-oscillator result. The latter arises only if the zero-damping limit is taken before the infinite-system limit.