On Consistency between Lagrange and Hamilton Formalisms in Quantum Mechanics

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Abstract
Consistency between the Lagrangean and the Hamiltonian formalisms in the quantum mechanics is investigatedc for the type of Lagrangean L=½\dotqigij(q)\dotqj-v(q) as an extension of a previous paper. The variations δqi and δ\dotqi should be considered as q-numbers. When the Lagrangean can be transformed into the standard form L=½\dotQα2-V(Q), the commutation relations of δqi and δ\dotqi with qj and \dotqj are found with the help of the Q-coordinate system. It is shown that using the commutation relations, the variation principle leads to the same equation of motion as the canonical equation of motion which is obtained in the previous paper.

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