Problem 6.96

Using Eq. (6.2e), find the probability \(D\) of a particle of mass \(m\) and energy \(E\) tunnelling through the potential barrier shown in Fig. \(6.6,\) where \(U(x)=U_{0}\left(1-x^{2} / l^{2}\right)\).

Reveal Answer

D \approx \exp \left[-\frac{\pi l}{\hbar} \sqrt{\frac{2 m}{U_{0}}}\left(U_{0}-E\right)\right]

Wave Properties of particles. Schrodinger Equation.