Abstract
Since the ordinary e-n umber variation principle does not lead, for a non-linear Lagrangian, to the result consistent between the Lagrangian and Hamiltonian formalisms, Schwinger's variation principle is reformulated for a type of Lagrangian L=tti(Jo(q)qi-u(q) by means of a q-number variation. The canonical momentum, the Hamiltonian, the canonical commuta tion relations and equation of motion are derived. Also the Euler-Lagrange equation is obtained, which is consistent with the canonical equation of motion. These consequences are exactly the same as those of previous papers, but different from the ordinary ones in the Euler-Lagran~e equation and the Hamiltonian.
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