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Chapter 6: Q15E (page 224)

Calculate the reflection probability 5evfor an electron encountering a step in which the potential drop by 2ev

Short Answer

Expert verified

The reflection probability is 0.007

Step by step solution

01

Definition of Reflection Probability

Reflection probability or reflection coefficient is defined as the ratio of amplitude of reflected wave to that of incident wave.

R=k2-k1k2+k12

Where, localid="1657549250276" k2=2m(E-v0)2 andk1=2mE2

02

Given/known parameters

E=5eV andV0=2eV

03

Solution

Substituting the values in the formula:

R=5-(-2)-55-(-2)+52

R=0.007

04

Explanation and Conclusion

The reflection probability is 0.007,i.e., there is0.7% chance of particle being reflected back.

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Most popular questions from this chapter

Question: Obtain equation (6.18) from(6.16) and (6.17).

Consider a potential barrier of height 30eV. (a) Find a width around1.000nmfor which there will be no reflection of 35eVelectrons incident upon the barrier. (b) What would be the reflection probability for 36eVelectrons incident upon the same barrier? (Note: This corresponds to a difference in speed of less than1(1/2)%.

As we learned in example 4.2, in a Gaussian function of the form蠄(x)伪e-(x2/2蔚2)is the standard deviation or uncertainty in position.The probability density for gaussian wave function would be proportional to蠄(x)squared:e-(x2/2蔚2). Comparing with the timedependentGaussian probability of equation (6-35), we see that the uncertainty in position of the time-evolving Gaussian wave function of a free particle is given by

.螖x=蔚1+h2t24m2蔚4 That is, it starts atand increases with time. Suppose the wave function of an electron is initially determined to be a Gaussian ofuncertainty. How long will it take for the uncertainty in the electron's position to reach5鈥�m, the length of a typical automobile?

Particles of energy Eare incident from the left, where U(x)=0, and at the origin encounter an abrupt drop in potential energy, whose depth is -3E.

  1. Classically, what would the particles do, and what would happen to their kinetic energy?
  2. Apply quantum mechanics, assuming an incident wave of the form蠄inc=eikx, where the normalization constant has been given a simple value of 1, determine completely the wave function everywhere, including numeric values for multiplicative constants.
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What fraction of a beam of 50eVelectrons would get through a 200V1nm wide electrostatic barrier?
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