Probability of tunneling through potential barriers in more than one dimension

C. Richard Leavens, G. C. Aers

Glen L. Goodvin, Mark R. A. Shegelski

We study a diatomic homonuclear molecule incident upon a potential barrier in three dimensions. We study various initial states for the molecule and allow transitions between rotational states of the molecule during the process of tunneling. By applying an elegant method to solve this problem we show that transmission resonances occur in several cases and that adding more binding energy levels for the molecule can tend to decrease the probability of tunneling. We also find that the probability of transmission can be enhanced by the addition of a second potential barrier. These results are in qualitative agreement with those found for the tunneling of a molecule in a one-dimensional model studied previously.

Mark R. A. Shegelski, Joshua Pittman, Rob Vogt +2 more

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.

Donald J. Le Roy, Richard Roy, K. A. Quickert

Rocco Schiavilla

Scattering in one dimension is discussed in terms of wave packets; reflection, transmission, and tunneling probabilities are defined; the WKB method to calculate these probabilities is introduced; the S-matrix for scattering in one dimension is defined; the phase-shift method for one-dimensional parity-invariant potentials is introduced; applications to various combinations of finite and infinite barriers with delta-function potentials are examined.

M. V. Bazilevskii