On Consistency between Lagrange and Hamilton Formalisms in Quantum Mechanics : Case of Non-Relativistic Velocity-Dependent Potential
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概要
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Consistency between the Lagrangean and the Hamiltonian formalisms in the quantum mechanics is investigated for the type of Lagrangean L=1/2q^^・_<ij>(q)q^^・_j-υ(q) as an extension of a previous paper. The variations δq_i and δq_i should be considered as q-numbers. When the Lagrangean can be transformed into the standard form L=1/2Q_α^2, the commutation relations of δq_i and δq_i with q_j and q_j 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.
- 理論物理学刊行会の論文
- 1971-07-25
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