All Problems

Wave Properties of particles. Schrodinger Equation.

Problem 6.96

Using Eq. (6.2e), find the probability DD of a particle of mass mm and energy EE tunnelling through the potential barrier shown in Fig. 6.6,6.6, where U(x)=U0(1−x2/l2)U(x)=U_{0}\left(1-x^{2} / l^{2}\right).

Reveal Answer
D≈exp⁡[−πlℏ2mU0(U0−E)]D \approx \exp \left[-\frac{\pi l}{\hbar} \sqrt{\frac{2 m}{U_{0}}}\left(U_{0}-E\right)\right]
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