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We introduce a self-adjoint operator that indicates the direction of timewithin the framework of standard quantum mechanics. That is, as a function oftime its expectation value decreases monotonically for any initial state. Thisoperator can be defined for any system governed by a Hamiltonian with auniformly finitely degenerate, absolutely continuous and semibounded spectrum.We study some of the operator's properties and illustrate them for a largeequivalence class of scattering problems. We also discuss some previousattempts to construct such an operator, and show that the no-go theoremsdeveloped in this context are not applicable to our construction.

An Arrow of Time Operator for Standard Quantum Mechanics