91影视

| FIGURE EX$40.4$ shows the wave function of an electron in a rigid box. The electron energy islocalid="1650137157775" $12.0eV$. What is the energy, in localid="1650137162096" $eV$, of the next higher state?

A proton鈥檚 energy is $1.0MeV$ below the top of a $10fm$-wide energy barrier. What is the probability that the proton will tunnel through the barrier?

a. What is the probability that an electron will tunnel through a$0.50nm$air gap from a metal to a STM probe if the work function is $4.0eV$?

b. The probe passes over an atom that is$0.050nm$鈥渢all.鈥� By what factor does the tunneling current increase?

c. If a $10\%$current change is reliably detectable, what is the smallest height change the STM can detect?

Consider a quantum harmonic oscillator.

a. What happens to the spacing between the nodes of the wave function as |x| increases? Why?

b. What happens to the heights of the antinodes of the wave function as |x| increases? Why?

c. Sketch a reasonably accurate graph of the n=8 wave function of a quantum harmonic oscillator.

a. Sketch graphs of the probability density ${\left|蠄\left(x\right)\right|}^2$for the four states in the finite potential well of Figure $40.14$a. Stack them vertically, similar to the Figure $40.14$a graph of $蠄x$.

b. What is the probability that a particle in the$n=2$ state of the finite potential well will be found at the center of the well? Explain.

c. Is your answer to part b consistent with what you know about standing waves? Explain.