Interaction of a Quantum System with a Strong Oscillating Field

Author: Shirley, Jon Hardy

Year: 1963

Degree: Dissertation (Ph.D.)

Advisor: Mathews, Jon

Committee Member: Unknown, Unknown

Option: Physics; Mathematics

DOI: 10.7907/3C1R-TG21

Abstract

The problem of the interaction of a quantum system having discrete states, with a classical oscillating field, is reexamined as a problem in the solution of the time-dependent Schrodinger equation with a periodic Hamiltonian. A method is presented for approximating the time-dependent Hamiltonian with a time-independent one in the weak oscillating field case. With the aid of Floquet's theorem the problem is exactly converted to one with a time-independent Hamiltonian represented by an infinite matrix. The approximation of only two states then permits finding the resonance line shape by perturbation theory for both single and multiple quantum transitions with equal ease. The simple case of only two states connected by an off diagonal sinusoidal perturbation is studied in detail, and a complete description of the average transition probability is found for the strong oscillating field case. A few more complex cases are discussed. A deeper understanding of the analysis is obtained by examining the theory with the oscillating field quantized. Experimental verification of the theory could best be obtained by the methods of atomic beam spectroscopy at radio frequencies.

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