Yongqin Wang, Lifeng Kang
A new mathematical method is established to represent the operator, wave functions and square matrix in the same representation. We can obtain the specific square matrices corresponding to the angular momentum and Runge-Lenz vector operators with invoking assistance from the operator relations and the orthonormal wave functions. Furthermore, the first-order differential equations will be given to deduce the specific wave functions without using the solution of the second order Schrodinger equation. As a result, we unified the descriptions of the matrix mechanics and the wave mechanics on hydrogen atom. By using matrix transformations, we will also deduce the specific matrix representations of the operators in the SO (4,2) group.
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http://arxiv.org/abs/1201.0136
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