This algebraic description is formulated in terms of two operator equations.
2.
The set of two operator equations, first derived and published by Brown and Hiley in 2000, was re-derived
3.
Hersh has written a number of technical articles on partial differential equations, probability, random evolutions, and linear operator equations.
4.
Since this is a vector and operator equation, if " ? " is an eigenfunction, then each component of the momentum operator will have an eigenvalue corresponding to that component of momentum.
5.
Which converts the operator equation to a matrix equation determining the unknown coefficients " c j " in terms of the generalized Fourier coefficients \ langle f _ j | h \ rangle of " h " and the matrix elements O _ { ji } = \ langle f _ j | O | e _ i \ rangle of the operator " O ".
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