Franz Schwabl Quantum Mechanics 4th Edit · Problem 3.9

The Uncertainty Relation

Physics — Quantum Mechanics · tunneling-time-gaussian-wave-packet

Problem

A one-dimensional, narrow Gaussian wave packet is scattered from a high potential barrier V0V_0 of width 2a2a. p022m≪V0 ,Δpp0≪1 .\frac{p_0^2}{2m} \ll V_0 \ , \quad \frac{\Delta p}{p_0} \ll 1 \ . Compute the time tpt_\mathrm{p} required for the packet to penetrate the potential barrier. Hint: Expand the transmission coefficient in the limit a2m(V0−E)/ℏ≫1 .a\sqrt{2m(V_0 - E)}/\hbar \gg 1 \ . Result: tp=ℏV0Et_\mathrm{p} = \frac{\hbar}{\sqrt{V_0 E}}

Browse the problem library