91影视

Exercise 54 gives a rough lifetime for a particle trapped particle to escape an enclosure by tunneling.

(a) Consider an electron. Given that$\mathbf{W}\mathbf{=}\mathbf{100}\mathbf{\text{鈥塶尘}}\mathbf{,}\mathbf{\text{鈥�}}\mathbf{L}\mathbf{=}\mathbf{1}\mathbf{\text{鈥塶尘鈥夆�塧nd鈥夆��}}{\mathbf{U}}_{\mathbf{0}}\mathbf{=}\mathbf{5}\mathbf{\text{鈥塭痴}}$, first verify that the${\mathbf{E}}_{\mathbf{GS}}\mathbf{<}\mathbf{<}{\mathbf{U}}_{\mathbf{0}}$assumption holds, then evaluate the lifetime.

(b) Repeat part (a), but for a$\mathbf{0}\mathbf{.}\mathbf{1}\mathbf{碌}\mathbf{g}$particle, with$\mathbf{W}\mathbf{=}\mathbf{1}\mathbf{nm}\mathbf{,}\mathbf{\text{鈥�}}\mathbf{L}\mathbf{=}\mathbf{1}\mathbf{碌}\mathbf{m}$, and a barrier height${\mathbf{U}}_{\mathbf{0}}$that equals the energy the particle would have if its speed were just$\mathbf{1}\mathbf{\text{鈥尘尘辫别谤测别补谤}}$.

Exercise 39 gives a condition for resonant tunneling through two barriers separated by a space width of$\mathbf{2}\mathbf{s}$, expressed I terms of factor$\mathbf{尾}$given in exercise 30. Show that in the limit in which barrier width$\mathbf{L}\mathbf{鈫�}\mathbf{鈭�}$, this condition becomes exactly energy quantization condition (5.22) for finite well. Thus, resonant tunneling occurs at the quantized energies of intervening well.

Your friend has just finished classical physics and can鈥檛 wait to know what lies ahead. Keeping extraneous ideas and postulates to a minimum, Explain the process of Quantum-mechanical tunneling.

How should you answer someone who asks, 鈥淚n tunneling through a simple barrier, which way are particles moving, in the three regions--before, inside, and after the barrier?鈥�

Given the same particle energy and barrier height and width, which would tunnel more readily: a proton or an electron? Is this consistent with the usual rule of thumb governing whether classical or non-classical behavior should prevail?

A ball is thrown straight up at $\mathbf{25}\mathbf{}\mathit{m}\mathit{s}\mathbf{-}\mathbf{1}$. Someone asks 鈥淚gnoring air resistance. What is the probability of the ball tunneling to a height of$\mathbf{}\mathbf{1000}\mathbf{}$$\mathit{m}$?鈥� Explain why this is not an example of tunneling as discussed in this chapter, even if the ball were replaced with a small fundamental particle. (The fact that the potential energy varies with position is not the whole answer-passing through nonrectangular barriers is still tunnelirl8.)

In the wide-barrier transmission probability of equation $\mathbf{(}\mathbf{6}\mathbf{-}\mathbf{18}\mathbf{)}$, the coefficient multiplying the exponential is often omitted. When is this justified, and why?