Quantum Theory of a Radiating Harmonically Bound Charge

Emilio Fiordilino
DOI: 10.4236/jmp.2010.14040                

Abstract

A phenomenological Hamiltonian giving the equation of motion of a non relativistic charges that accelerates and radiates is quantized. The theory is applied to the harmonic oscillator. To derive the decay time the physical parameters entering the calculations are obtained from the theory of the hydrogen atom; the agree- ment of the predicted value with the experiments is striking although the mathematics is very simple.

Keywords

Radiation Damping, Quantum Radiation, Phenomenological Hamiltonian

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	P. A. M. Dirac, “Classical Theory of Radiating Electrons,” Proceedings of the Royal Society A, Vol. 167, No. 929, 1938, pp. 148-169.
[2]	J. A. Wheeler and R. P. Feynman, “Interaction with the Absorber as the Mechanism of Radiation,” Reviews of Modern Physics, Vol. 17, No. 2-3, 1945, pp. 157-181
[3]	G. N. Plass, “Classical Electrodynamic Equations of Motion with Radiative Reaction,” Reviews of Modern Physics, Vol. 33, No. 1, 1961, pp. 37-62.
[4]	F. Rohrlich, “Dynamics of a Charged Particle,” Physical Review E, Vol. 77, No. 4, 2008, p. 46609.
[5]	A. D. Piazza, “Exact Solution of the Landau-Lifshitz Equation in a Plane Wave,” Letters in Mathematic Physics, Vol. 83, No. 3, 2008, pp. 305-313.
[6]	P. W. Milonni, J. R. Ackerhalt and W. A. Smith, “Interpretation of Radiative Corrections in Spontaneous Emission,” Physical Review Letters, Vol. 31, No. 15, 1973, p. 958.
[7]	J. J. Sakurai, “Advanced Quantum Mechanics,” Addison- Wesley, Reading, London, 1982.
[8]	Z. Chang, A. Rundquist, H. Wang, M. M. Murnane and H. C. Kapteyn, “Generation of Coherent Soft X Rays at 2.7 nm Using High Harmonics,” Physical Review Letters, Vol. 79, No. 16, 1997, pp. 2967-2970.
[9]	K. W. H. Stevens, “The Wave Mechanical Damped Harmonic Oscillator,” Proceedings of Physical Society, Vol. 72, No. 6, 1958, p. 1027.
[10]	K. W. H. Stevens and B. Josephson Jr, “The Coupling of a Spin System to a Cavity Mode,” Proceedings of Physical Society, Vol. 74, No. 5, 1959, p. 561.
[11]	J. R. Ray, “Lagrangians and Systems they Describe-How Not to Treat Dissipation in Quantum Mechanics,” American Journal of Physics, Vol. 47, No. 7, 1979, p. 626.
[12]	V. W. Myers, “Quantum Mechanical Treatment of Systems with a Damping Force Proportional to the Velocity,” American Journal of Physics, Vol. 27, No. 7, 1959, pp. 507-508.
[13]	L. H. Buch and H. H. Denman, “Solution of the Schr?dinger Equation for Some Electric Problems,” American Journal of Physics, Vol. 42, No. 4, 1974, pp. 304-309.
[14]	P. P. Corso, E. Fiordilino and F. Persico, “Direct Theoretical Evidence of Nuclear Motion in by Means of High Harmonic Generation,” Journal of Physics B: Atomic. Molecular and Optical Physics, Vol. 40, No. 7, 2007, p. 1383.