Confined Quantum Time of Arrival for Vanishing Potential
arXiv:quant-ph/0512096 · doi:10.1103/PhysRevA.72.062107
Abstract
We give full account of our recent report in [E.A. Galapon, R. Caballar, R. Bahague {\it Phys. Rev. Let.} {\bf 93} 180406 (2004)] where it is shown that formulating the free quantum time of arrival problem in a segment of the real line suggests rephrasing the quantum time of arrival problem to finding a complete set of states that evolve to unitarily arrive at a given point at a definite time. For a spatially confined particle, here it is shown explicitly that the problem admits a solution in the form of an eigenvalue problem of a class of compact and self-adjoint time of arrival operators derived by a quantization of the classical time of arrival. The eigenfunctions of these operators are numerically demonstrated to unitarilly arrive at the origin at their respective eigenvalues.
arXiv commentaccepted for publication in Phys. Rev. A
References in corpus (19)
- Time-of-arrival in quantum mechanics
- Arrival time in quantum mechanics
- Positive-Operator-Valued Time Observable in Quantum Mechanics
- Pauli's Theorem and Quantum Canonical Pairs: The Consistency Of a Bounded, Self-Adjoint Time Operator Canonically Conjugate to a Hamiltonian with Non-empty Point Spectrum
- A measurement-based approach to quantum arrival times
- Confined Quantum Time of Arrivals
- Free motion time-of-arrival operator and probability distribution
- Time-of-arrival distribution for arbitrary potentials and Wigner's time-energy uncertainty relation
- Space-time properties of free motion time-of-arrival eigenstates
- Time of occurrence observable in quantum mechanics
- Self-adjoint Time Operator is the Rule for Discrete Semibounded Hamiltonians
- Localization of Events in Space-Time
- Time of arrival in the presence of interactions
- Transition from discrete to continuous time of arrival distribution for a quantum particle
- Quantum arrival times and operator normalization
- Operator normalized quantum arrival times in the presence of interactions
- Time-of-arrival distributions from position-momentum and energy-time joint measurements
- Quantum times of arrival for multiparticle states
- Comment on "Measurement of time of arrival in quantum mechanics"
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- A one-particle time of arrival operator for a free relativistic spin-0 charged particle in (1+1) dimensions
- Quantum Operations: technical or fundamental challenge?
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