Generalized probability and current densities: A Field theory

Abstract

We introduce a generalized Lagrangian density - involving a non-Hermitian kinetic term - for a quantum particle with the generalized momentum operator. Upon variation of the Lagrangian, we obtain the corresponding Schrödinger equation. The extended probability and particle current densities are found which satisfy the continuity equation.

9 pages. arXiv admin note: substantial text overlap with arXiv:2102.02565