Generalized crossing states in the interacting case: The uniform gravitational field
- Theoretical Physics Group, National Institute of Physics, University of the Philippines, Diliman Quezon City, 1101 Philippines (Philippines)
We reconsider Baute et al.'s free crossing states [Phys. Rev. A 61, 022118 (2000)] and show that if we require a generalization in the interacting case that goes in complete parallel with the free-particle case, then this generalized crossing state cannot be arbitrary but is determined by the null space of the particle's quantum time-of-arrival operator. Nonetheless, the free crossing states appear as the leading term in the asymptotic expansion of our generalized crossing state in the limit of large momentum. We then examine the quantum time-of-arrival problem of a spinless particle in a uniform gravitational field. Mass-dependent time-of-arrival probability distributions emerge, signifying quantum departures from the weak equivalence principle. However, in the classical limit of large mass and vanishing uncertainty in position, the mass dependence of the quantum time-of-arrival distribution becomes exponentially small and the mean quantum time of arrival reduces to the classical time of arrival.
- OSTI ID:
- 21528574
- Journal Information:
- Physical Review. A, Vol. 82, Issue 5; Other Information: DOI: 10.1103/PhysRevA.82.052117; (c) 2010 The American Physical Society; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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