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Full-Text Articles in Physical Sciences and Mathematics
Mielnik Probability Spaces And Functional Equations, J. J. Mitchell
Mielnik Probability Spaces And Functional Equations, J. J. Mitchell
Opportunities for Undergraduate Research Experience Program (OURE)
The invariance properties of the solutions of those functional equations naturally occurring in the construction of Mielnik probability spaces are studied, and in turn are related to one another. In particular, the possibilities for fixed points of these solutions are found, and the relationships between these results are discussed. The two functional equations studied include a representation of the generalized parallelogram law and an equation used in the modeling of polarization phenomena. The main result of the paper lies in the extention of previous research on Mielnik probability spaces to a higher dimension, as well as a discussion of their …
Shooting Method Solutions Of Eigenvalue Problems, Xi Chen
Shooting Method Solutions Of Eigenvalue Problems, Xi Chen
Opportunities for Undergraduate Research Experience Program (OURE)
A shooting method was developed to study eigenvalue problems derived from Schrodinger equation. The challenging problem, the two-dimensional hydrogen system with the logarithmic potential function, was successfully solved by the shooting method. But no complete proof was given for its rationale and correctness. This paper not only gives the complete proof for the shooting method, but also generalizes it to solve a large class of eigenvalue problems. In a certain sense, the shooting method proves more effective numerically and more powerful theoretically than the classical functional analysis approach.