Abstract This article examines resonant tunnelling of multi-atomic systems, extending the body of work on resonant tunnelling in this area beyond diatomic homo-nuclear systems. We consider diatomic molecules with distinct atoms having different masses, and linear triatomic molecules with indistinguishable atoms. The molecule is incident in the bound state upon a step potential with an energy increase of V 0 for each atom. We calculate the probabilities of reflection p R and transmission p T in the bound state and the dependence on the energy of the molecule. We find that, as was the case for the homo-nuclear molecule, resonant transmission for diatomic molecules with distinguishable atoms occurs for arbitrarily weak binding, and p T is close to one for finite binding energy. We also find resonant transmission for linear triatomic molecules. We show results for the time-dependent Schrödinger equation which agree with resonant transmission. We also consider the transmission of an N -atom one-dimensional molecule.
We study in three dimensions a diatomic homo-nuclear molecule with many bound states incident upon a potential barrier. We consider different initial states for the molecule and take into account transitions between rotational states of the molecule during the process in which the entire molecule tunnels past or is reflected by the external potential barrier. We show the manner in which the transmission resonances are affected by having many bound states. We find that the transmission probability profile in three dimensions is markedly different from that for two bound states in three dimensions, and for many bound states in one dimension. We find important new results. One result is that resonant or near resonant tunnelling and resonant or near resonant reflection can both occur within a small energy range of the molecule. We also find that tunnelling with transmission probability close to unity can occur over a wide energy range.
Abstract The case of a molecule with a single weakly bound state is considered. The molecule is incident in the bound state upon a step potential with an energy increase of V 0 . We calculate the probability of reflection p R and transmission p T in the bound state and its dependence on the energy of the molecule. Three energy ranges are examined. For the highest range, resonant transmission occurs for all energies, a behaviour drastically different than that of a single particle. Other unexpected results are obtained and the physical reasons underlying the results are discussed.
We study the effects of multiple bound states on the probability of tunneling of a homonuclear diatomic molecule incident upon a potential barrier in one dimension. We obtain additional bound states by several means: by varying individual features of the binding potential as well as increasing the mass of the two atoms. We find that the tunneling behavior of a molecule with a large number of bound states $(\ensuremath{\sim}30)$ is drastically different from that for a molecule with a small number of states $(\ensuremath{\lesssim}5)$. Further, we find that the effect of multiple bound states on the proabability of tunneling is largely dependent upon the separation between the bound-state energies. It is also found that intermediary transitions between many bound states results in significantly larger reductions in the probability of tunneling. Finally, we investigate molecules of different masses and observe common qualitative features. We focus on molecules incident upon a $\ensuremath{\delta}$ barrier but we also consider Gaussian barriers.
We investigate, in one spatial dimension, the quantum mechanical tunnelling of a diatomic, homogeneous molecule with a single bound state incident upon an external barrier. Both time-independent and time-dependent tunnelling are investigated, using analytical and numerical methods. In the time-independent case, we first derive a formal solution for the molecule's wave function. Then, using the method of variable reflection and transmission amplitudes, we find that the probabilities of reflection and transmission in the bound state decrease with decreased binding strength, while the probabilities of refection and transmission in an unbound state increase with decreased binding energy. In the time-dependent case, we consider a molecule with discrete unbound states. 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, in addition to reflecting and transmitting, the molecule may also straddle the potential barrier in an unbound state.
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
e0 approaches zero and the step potential
V0 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
x0 which increases as the magnitude of
e0 decreases, as
V0 increases, or both. We also show that, for ${e}_{0}\ensuremath{\rightarrow}{0}^{\ensuremath{-}}$ and ${V}_{0}\ensuremath{\rightarrow}\ensuremath{\infty}$, 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
x0. 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.
We study the reflection and transmission of a homonuclear diatomic molecule incident upon a potential barrier in one dimension. The effect of discrete and continuous unbound molecular states is investigated. We use the method of variable reflection and transmission amplitudes for discrete unbound states and we extend the method to include continuous unbound states. We take into account transitions between the bound and unbound states in the process of tunneling. For the molecule incident in a bound state, we calculate the probabilities of reflection and transmission in bound states as well as in unbound states. We focus on the molecule incident upon a $\ensuremath{\delta}$ barrier but we also investigate rectangular and Gaussian barriers. We show that transmission resonances are appreciably reduced by the inclusion of unbound states due to the lack of resonant structure in the probabilities of reflection and transmission in unbound states. We also find that much of the behavior of the molecule in the process of tunneling is primarily due to the bound states.