Relativistic free motion time of arrival operator for massive spin-0 particles with positive energy
arXiv:2203.00898 · doi:10.1103/PhysRevA.105.062208
Abstract
A relativistic version of the Aharonov-Bohm time of arrival operator for spin-0 particles was constructed by Razavi in [Il Nuovo Cimento B \textbf{63}, 271 (1969)]. We study the operator in detail by taking its rigged Hilbert space extension. It is shown that the rigged Hilbert space extension of the operator provides more insights into the time of arrival problem that goes beyond Razavi's original results. This allows us to use time of arrival eigenfunctions that exhibit unitary arrival to construct time of arrival distributions. The expectation value is also calculated and shown that particles can arrive earlier or later than expected classically. Lastly, the constructed time of arrival distribution, and expectation value are shown to be consistent with special relativity.
References in corpus (27)
- Problem of Time in Quantum Gravity
- Time-of-arrival in quantum mechanics
- Arrival time 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
- Free motion time-of-arrival operator and probability distribution
- Confined Quantum Time of Arrivals
- Space-time properties of free motion time-of-arrival eigenstates
- Time-of-arrival formalism for the relativistic particle
- Transition from discrete to continuous time of arrival distribution for a quantum particle
- Time in quantum physics: From an external parameter to an intrinsic observable
- Shouldn't there be an antithesis to quantization?
- A dynamical time operator in Dirac's relativistic quantum mechanics
- Confined Quantum Time of Arrival for Vanishing Potential
- Rigged Hilbert Space Approach to the Schrodinger Equation
- The Cauchy Principal Value and the finite part integral as values of absolutely convergent integrals
- Space-time symmetric extension of non-relativistic quantum mechanics
- Quantizations of the classical time of arrival and their dynamics
- Quantum Traversal Time Across a Potential Well
- Quantum free fall motion and quantum violation of weak equivalence principle
- The Rigged Hilbert Space of the Free Hamiltonian
- Comparing experiments on quantum traversal time with the predictions of a space-time-symmetric formalism
- Relativistic free-motion time-of-arrival
- A one-particle time of arrival operator for a free relativistic spin-0 charged particle in (1+1) dimensions
- Arrival Time in Relativistic Quantum Mechanics
- A Relativistic One-Particle Time of Arrival Operator for a Free Spin-1/2 Particle in (1 + 1) Dimensions
- Time and energy operators in the canonical quantization of special relativity
- Synchronizing quantum and classical clocks made of quantum particles