TITLE:
On the Crucial Role of the Variational Principle in Quantum Theories
AUTHORS:
Eliahu Comay
KEYWORDS:
Quantum Theories, Lagrangian Density, Corpuscular-Wave Duality, Dimension of the Quantum Function, The Correspondence Principle
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.5 No.11,
November
3,
2017
ABSTRACT: The paper shows that the variational principle serves as an element of the mathematical structure of a quantum theory. The experimentally confirmed properties of the corpuscular-wave duality of a quantum particle are elements of the analysis. A Lagrangian density that yields the equations of motion of a given quantum theory of a massive particle is analyzed. It is proved that if this Lagrangian density is a Lorentz scalar whose dimension is then the associated action consistently defines the required phase of the quantum particle. The dimension of this Lagrangian density proves that also the quantum function has dimension. This result provides new criteria for the acceptability of quantum theories. An examination of the first order Dirac equation demonstrates that it satisfies the new criteria whereas the second order Klein-Gordon equation fails to do that.