Q-Number Variational Method for Non-Linear Lagrangian in Quantum Mechanics
Open Access
- 1 November 1973
- journal article
- Published by Oxford University Press (OUP) in Progress of Theoretical Physics
- Vol. 50 (5) , 1715-1728
- https://doi.org/10.1143/ptp.50.1715
Abstract
A previous q-number variational method is extended to be applicable to any quantum system for which the classical Lagrangian is given by Lc=½gij\dotqi\dotqj+ui\dotqi-v. The q-number variation is necessary for the formulation to be form-invariant under a general space-time transformation. From the action principle, not only the Euler-Lagrange equation but also the commutation relations up to a constant factor are obtained. Futhermore the form of the quantum Lagrangian is, to some extent, decided in order for solutions to exist for the action principle. It is shown that the first Noether theorem holds and the quantization is consistent with the canonical formalism.Keywords
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