2016•Journal of Mathematical PhysicsRequires access

A symmetric time-like operator

Gabino Torres-Vega

Abstract

We introduce an operator which is the difference between the derivative to the right and to the left, times iħ, intended to be used in non-relativistic quantum mechanics. This operator is a symmetric, independently of boundary conditions, proposal to a time operator. Some properties of this operator are derived and their eigenstates are found for the free particle system.

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Key concepts: Operator (biology), Displacement operator, Momentum operator, Ladder operator, Eigenvalues and eigenvectors, Mathematics, Shift operator, Position operator