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Interaction of a quantum system with a strong oscillating field

Citation

Shirley, Jon H. (1963) Interaction of a quantum system with a strong oscillating field. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-05142008-103758

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.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Mathews, Jon
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1963
Record Number:CaltechETD:etd-05142008-103758
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-05142008-103758
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1805
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:14 May 2008
Last Modified:26 Dec 2012 02:42

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