Free-fall in a uniform gravitational field in noncommutative quantum mechanics

Journal Article · Fri Oct 15 04:00:00 EDT 2010 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3466812· OSTI ID:21476570

Castello-Branco, K H. C. ^[1]; Martins, A G ^[2]

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1. Instituto de Fisica de Sao Carlos, Universidade de Sao Paulo, Av. Trabalhador Sao-Carlense, 400, Sao Carlos, Sao Paulo 13560-970 (Brazil)
2. Departamento de Ciencias Naturais, Universidade do Estado do Para, Av. Djalma Dutra, s/n, Belem, Para 66113-200 (Brazil)

We study the free-fall of a quantum particle in the context of noncommutative quantum mechanics (NCQM). Assuming noncommutativity of the canonical type between the coordinates of a two-dimensional configuration space, we consider a neutral particle trapped in a gravitational well and exactly solve the energy eigenvalue problem. By resorting to experimental data from the GRANIT experiment, in which the first energy levels of freely falling quantum ultracold neutrons were determined, we impose an upper-bound on the noncommutativity parameter. We also investigate the time of flight of a quantum particle moving in a uniform gravitational field in NCQM. This is related to the weak equivalence principle. As we consider stationary, energy eigenstates, i.e., delocalized states, the time of flight must be measured by a quantum clock, suitably coupled to the particle. By considering the clock as a small perturbation, we solve the (stationary) scattering problem associated and show that the time of flight is equal to the classical result, when the measurement is made far from the turning point. This result is interpreted as an extension of the equivalence principle to the realm of NCQM.

• OSTI ID: 21476570
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 10 Vol. 51; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BARYONS
COLD NEUTRONS
COMMUTATION RELATIONS
EIGENFUNCTIONS
EIGENSTATES
EIGENVALUES
ELEMENTARY PARTICLES
ENERGY LEVELS
EQUIVALENCE PRINCIPLE
FERMIONS
FIELD THEORIES
FUNCTIONS
GRAVITATIONAL FIELDS
HADRONS
MECHANICS
NEUTRAL PARTICLES
NEUTRONS
NUCLEONS
PERTURBATION THEORY
QUANTUM FIELD THEORY
QUANTUM GRAVITY
QUANTUM MECHANICS
SCATTERING
TIME-OF-FLIGHT METHOD
TRAPPING
TWO-DIMENSIONAL CALCULATIONS
ULTRACOLD NEUTRONS