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Chapter 6: Q3CQ (page 223)

Why is the topic of normalization practically absent from Sections 6.1 and 6.2?

Short Answer

Expert verified

We don’t normalize with multiple particles as with a single particle.

Step by step solution

01

Definition of normalization

Normalization is defined as the scaling of all wave functions of a quantum state to an exact form such that all probabilities of finding a particle anywhere in space add up to 1.

02

Explanation and conclusion

In this section, plane waves are used for the representation of a single particle or a group of particles behaving as one coherent wave and studying its reflection and transmission coefficients. For multiple particles, we usually don’t normalize for unit probability but seek the multiplicative coefficients.

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Most popular questions from this chapter

A beam of particles of energy E incident upon a potential step of $U_{0} = (5 / 4)$ E is described by wave function: $ψ_{i n c} (x) = e^{i k x}$

Determine the reflected wave and wave inside the step by enforcing the required continuity conditions to obtain their (possibly complex) amplitudes.
Verify the explicit calculation the ratio of reflected probability density to the incident probability density is 1.

A method for finding tunneling probability for a barrier that is "wide" but whose height varies in an arbitrary way is the so-called WKB approximation.

$T = e x p [- \frac{2}{ℏ} \int_{1}^{2} \sqrt{2 m (U (x) - E)} d x]$

Here U(x) is the height of the arbitrary potential energy barrier.Whicha particle first penetrates at x=0 and finally exits at x=L. Although not entirely rigorous, show that this can be obtained by treating the barrier as a series of rectangular slices, each of width dx (though each is still a "wide" barrier), and by assuming that the probability of tunneling through the total is the product of the probabilities for each slice.

Verify that the reflection and transmission probabilities given in equation (6-7) add to 1.

Could the situation depicted in the following diagram represent a particle in a bound state? Explain.

What fraction of a beam of $50 e V$ electrons would get through a $200 V 1 n m$ wide electrostatic barrier?

See all solutions

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