TIME-INDEPENDENT HAMILTON LINEAR AND NONLINEAR CANONICAL TRANSFORMATION
Xiaobing Luo · Journal of Jinggangshan University · 2011
n order to solve Hamilton canonical transformation and seek cyclic coordinate,we introduce the linear and nonlinear canonical transformation.The results show that the new Hamiltonian after transformation is different strictly from the initial Hamiltonian by an addition of arbitrary function only of time.Due to the additional arbitrary function is nothing to do with Hamilton canonical equation,one can let the function to be zero.Thus the Hamiltonian remains unchanged in time-independent canonical transformation.For the time-independent linear canonical transformation,we introduce a transformation matrix M and prove the determinant of the matrix must equal to 1.It is almost impossible to get a cyclic coordinate by linear canonical transformation.For the time-independent nonlinear canonical transformation,different transformation matrix M has been introduced and proved that its determinant must equal to 1.One can always find a suitable nonlinear canonical transformation to produce a cyclic coordinate.