Narrow Results

We derive an expression for the conditional time for the reflection of a wave from an arbitrary potential barrier using the WKB wavefunction in the barrier region. Our result indicates that the conditional times for transmission and reflection are equal for a symmetric barrier within the validity of the WKB approach.

A state of an electron in a quantum wire or a thin film becomes metastable, when a static electric field is applied perpendicular to the wire direction or the film surface. The state decays via tunneling through the created potential barrier. An additionally applied magnetic field, perpendicular to the electric field, can increase the tunneling decay rate of an excited state by many orders of magnitude. This happens when the state in the wire or the film has a velocity perpendicular to the magnetic field. According to the cyclotron effect, the velocity rotates under the barrier and becomes more aligned with the direction of tunneling. This mechanism can be called cyclotron enhancement of tunneling.

We study the scattering of a Gaussian wave packet in the modified Pöschl–Teller potential well in time respect. Analytical expressions of average dwell time, phase time, and average traversal time due to Larmor-clock times are obtained, from which the average traversal time can be identified with the average dwell time. We observe that the average dwell time is appreciably longer than the phase time at low energies, but they tend to coincide in the limit of narrow momentum distribution, high energy, and large interaction region. We also find that both of them are longer than the classical scattering time in the potential. All of these times are, however, shorter than the free-particle time, demonstrating the acceleration effect of the potential in temporal aspect of the scattering.