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Wave Properties of particles. Schrodinger Equation.

Problem 6.95

Employing Eq. (6.2e),(6.2 \mathrm{e}), find the probability DD of an electron with energy EE tunnelling through a potential barrier of width ll and height U0U_{0} provided the barrier is shaped as shown: (a) in Fig. 6.4 (b) in Fig. 6.5 .

Reveal Answer
6.95. (a) D≈exp⁡[−2lℏ2m(U0−E)]D \approx \exp \left[-\frac{2 l}{\hbar} \sqrt{2 m\left(U_{0}-E\right)}\right] (b) D≈exp⁡[−8l2m3ℏU0(U0−E)3/2]D \approx \exp \left[-\frac{8 l \sqrt{2 m}}{3 \hbar U_{0}}\left(U_{0}-E\right)^{3 / 2}\right]
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