A quantum mechanical Boltzmann equation for a polyatomic gas in magnetic and electric fields

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
William Mebane Baker (Creator)
The University of North Carolina at Greensboro (UNCG )
Web Site: http://library.uncg.edu/
Francis McCormack

Abstract: This paper proposes to examine the process by which a quantum mechanical Boltzmann equation for a dilute polyatomic gas, involving only binary collisons, is developed. The method employed parallels the work of R. F. Snider (Journal of Chemical Physics, April, I960.), which is referenced throughout the text. Snider's procedure is extended to the case of a polyatomic gas in the presence of magnetic and electric fields, which may be time variant. Chapter 2 is devoted to describing a quantized system by use of the concepts of state vectors and state functions. The state vectors and functions are then used to develop the idea of system averaging; specifically the concept of expectation values. Chapter 3 extends the work of Chapter 2 in developing ensemble averaging from expectation values. The density matrix; is then defined by its relationship to the ensemble average for the operator, and the operator itself. In Chapter 4, the equation of motion for the density matrix is derived by employing the definition of the density matrix, developed in Chapter 3. The dilute nature of the gas is then used (i.e., use of the Boltzmann property) to rewrite the equation of motion in terms of the one and two particle density matrices. The problem is, thereby, greatly simplified.

Additional Information

Language: English
Date: 1972
Transport theory
Kinetic theory of gases
Equations of motion
Density matrices
Electric fields
Magnetic fields

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