International Conference on Numerical Analysis and Applied Mathematics, Rhodes, Greece, 19 - 25 September 2010, vol.1281, pp.1950-1951
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.