Time of occurrence observable in quantum mechanics

Positive - Operator - Valued Time Observable in Quantum Mechanics

We examine the longstanding problem of introducing a time observable in Quantum Mechanics; using the formalism of positive-operator-valued measures we show how to define such an observable in a natural way and we discuss some consequences.

Time as an operator/observable in nonrelativistic quantum mechanics

The nonrelativistic Schrödinger equation for motion of a structureless particle in four-dimensional space-time entails a well-known expression for the conserved four-vector field of local probability density and current that are associated with a quantum state solution to the equation. Under the physical assumption that each spatial, as well as the temporal, component of this current is observa...

Arrival Time in Quantum Mechanics

TIME DEPENDENCE in QUANTUM MECHANICS

Time-dependent perturbation theory is formulated in a systematic way. The focus is shifted from the wavefunction to the unitary transformation that evolves the wavefunction from one slice of time to another. Perturbation theory is formulated in terms of a systematic iterative expansion of the unitary transformation in terms of the perturbing hamiltonian, expressed in the interaction representat...

Time of arrival in quantum mechanics.

We study the problem of computing the probability for the time-of-arrival of a quantum particle at a given spatial position. We consider a solution to this problem based on the spectral decomposition of the particle's (Heisenberg) state into the eigenstates of a suitable operator, which we denote as the \time-of-arrival" operator. We discuss the general properties of this operator. We construct...