Quantum tunneling and reflection of a molecule with a single bound state

Journal Article · Mon Feb 15 00:00:00 EST 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.81.022708· OSTI ID:21408234

Kavka, Jeremy J; Kerbrat, Danielle; Shegelski, Mark R. A. ^[1]

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1. Department of Physics, University of Northern British Columbia, Prince George, British Columbia V2N 4Z9 (Canada)

In this article, we present the results of studies on the quantum mechanical tunneling and reflection of a diatomic, homonuclear molecule with a single bound state incident upon a potential barrier. In the first study, we investigate the tunneling of a molecule using a time-dependent formulation. The molecular wave function is modeled as a Gaussian wave packet, and its propagation is calculated numerically using Crank-Nicholson integration. It is found that a molecule may transition between the bound state and an unbound state numerous times during the process of reflection from or transmission past the barrier. It is also found that, in addition to reflecting and transmitting, the molecule may also temporarily straddle the potential barrier in an unbound state. In the second study, we consider the case of a molecule incident in the bound state upon a step potential with energy less than the step. We show that in the limit where the binding energy e{sub 0} approaches zero and the step potential V{sub 0} goes to infinity, the molecule cannot remain in a bound state if the center of mass gets closer to the step than an arbitrarily large distance x{sub 0} which increases as the magnitude of e{sub 0} decreases, as V{sub 0} increases, or both. We also show that, for e{sub 0{yields}}0{sup -} and V{sub 0{yields}{infinity}}, if the molecule is incident in the bound state, it is reflected in the bound state with probability equal to unity, when the center of mass reaches the reflection distance x{sub 0}. We verify that the unbound states exhibit the expected physical behavior. We discuss some surprising results. Connections between our results and investigations done in cold atoms, excitons, Cooper pairs, and Rydberg atoms are discussed.

• OSTI ID: 21408234
• Journal Information: Physical Review. A, Vol. 81, Issue 2; Other Information: DOI: 10.1103/PhysRevA.81.022708; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
ATOMS
BINDING ENERGY
BOUND STATE
CENTER-OF-MASS SYSTEM
COOPER PAIRS
DISTANCE
EXCITONS
MOLECULES
POTENTIALS
PROBABILITY
QUANTUM MECHANICS
REFLECTION
TIME DEPENDENCE
TUNNEL EFFECT
TUNNELING
WAVE FUNCTIONS
WAVE PACKETS
ENERGY
FUNCTIONS
MECHANICS
QUASI PARTICLES