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 0 approaches zero and the step potential V 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 0 which increases as the magnitude of e 0 decreases, as V 0 increases, or both. We also show that, for e 0 → 0 − and V 0 → ∞, 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 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.

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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.

We investigate, in one spatial dimension, the quantum mechanical tunneling of an exciton incident upon a heterostructure barrier. We model the relative motion eigenstates of the exciton using a form of the one-dimensional hydrogen atom which avoids difficulties previously associated with 1D hydrogenic states. We obtain probabilities of reflection and transmission using the method of variable transmission and reflection amplitudes. Our calculations may be broadly divided into two sets. In the first set, we consider general qualitative aspects of exciton tunneling, such as the effect of different effective masses for electrons and holes and a relative difference in electron and hole barrier strengths. The second set models the tunneling of an exciton in a GaAs/Al(x)Ga(1-x)As heterostructure. In these calculations we find that, for energies such that the two lowest exciton states are coupled, the probability spectrum for transition from the ground state to the first excited state is identical to that for transition from the first excited state to the ground state. In addition, narrow peaks in the probability spectrum for transition are observed across this energy range for low dopant concentration x. Other interesting phenomena correlated with these peaks in the transition probability are reported.

We present a method for calculating lifetimes without using semiclassical approximations by using a heuristic expression for the lifetime. The details are given for tunneling past a centrifugal barrier. We compare the fully quantum mechanical results to the well-known WKB tunneling times. We show that bound states play a major role in determining lifetimes.