Analysis of semiclassical wave transmission across a potential barrier highlights the role of energy differences and implications for transmission probability.
The probability of Schr"odinger wave transmission through a symmetric 1-dimensional potential barrier having a sharp top and otherwise arbitrary monotonically declining shape is evaluated in the uniform semiclassical approximation. In the →0 or straight wedge limit it reduces to a dependence on a single scale parameter proportional to the difference between the energy and the maximal value of the potential. When this difference equals zero, the wedge transmission probability equals 3/4, in contrast to the round-top potential case, for which it equals 1/2. A more accurate formula based on the uniform semiclassical approximation is derived, being valid under more general conditions. It involves the second derivative of the potential at the top, and if it is positive (a concave potential), it makes the energy dependence of the transmission probability steeper.
No takes yet. Share an insight, caveat, or question.
M. V. Bondarenco (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: