Construction of a Quantum Field Linked to the Coulomb Potential
We construct a non-Gaussian field and its associated creation and annihilation operators, describing non-interacting bound states with no momentum in a Coulomb potential. The system is shown to behave quantum mechanically as a collection of coupled harmonic oscillators, allowing us to construct the field by injection into the quantum mechanical space of a free Gaussian field, and to study its time development.
KeywordsCoulomb Potential Annihilation Operator Radial Wave Function Wick Product Couple Harmonic Oscillator
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- P. Carmona. Généralisation de la loi de l’arc sinus et entrelacements de processus de Markov. Thèse, Université de Paris VI, 1994.Google Scholar
- W. Feller. An Introduction to Probability Theory and its Applications, volume II. John Wiley and Sons, New York, 1966.Google Scholar
- J. Glimm and A. Jaffe. Quantum Physics, a Functional Integral Point of View. Springer Verlag, Berlin/New-York, 1987.Google Scholar