Nonlinear vector product for describing rotations in quantum physics
DOI:
https://doi.org/10.5902/2179460X24717Abstract
A method is developed for treating successive rotations in terms of nonlinear products of rotational vector. Combinations of ordinary scalar and vector products yield the same results that may be more commonly arrived at by the use of quaternions or 2x2 unitarymatrices. The method presented here, automatically provides us the direction of the axis and the value of the rotation angle of the single rotation that is equivalent to the product of two or more successive rotations. This information is not readily obtained from the usual matrix rotation method of solving the successive rotations problem. The method is applied to the case of a rotation abount the {111} direction, successive π rotations abount orthogonal axes, and the treatment of continuous rotations.
It also useful in Quantum Physics, Lorentz matrix representation and simmetry studies in solid state Physics.
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References
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