A Fluctuation Analysis at the Classical Limit for the Expectation Dynamics of a Single Quartic Quantum Anharmonic Oscillator
- Istanbul Technical University, Informatics Institute, Group for Science and Methods of Computing, Maslak, 34469, Istanbul (Turkey)
The definition of the fluctuation terms in the matrix representations of operators, especially function operators, brings a lot of facilitations to the numerical analysis of matrix representation issues. This work considers a one-dimensional quantum oscillator with purely quartic anharmonicity and focuses on its position and momentum expectations. By using certain level commutator operation it is possible to get two ODEs as equations of motion, which are in classical nature when the fluctuation terms are omitted. To understand how fluctuation terms affect expectation dynamical analysis we add extra temporal unknowns and construct extra ODEs over them. There seem to be an infinite ODEs chain for fluctuation altough their truncations seem to be utilizable as approximations. Here basic theory is summarized. Further details will be prasented at the conference presentation.
- OSTI ID:
- 21428584
- Journal Information:
- AIP Conference Proceedings, Vol. 1281, Issue 1; Conference: ICNAAM 2010: International conference of numerical analysis and applied mathematics 2010, Rhodes (Greece), 19-25 Sep 2009; Other Information: DOI: 10.1063/1.3498311; (c) 2010 American Institute of Physics; ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
ANHARMONIC OSCILLATORS
APPROXIMATIONS
COMMUTATORS
EQUATIONS OF MOTION
FLUCTUATIONS
FUNCTIONAL ANALYSIS
MATRICES
NUMERICAL ANALYSIS
ONE-DIMENSIONAL CALCULATIONS
OSCILLATORS
QUANTUM MECHANICS
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
ELECTRONIC EQUIPMENT
EQUATIONS
EQUIPMENT
MATHEMATICAL OPERATORS
MATHEMATICS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS
VARIATIONS