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Chapter 39: Q 10 Exercise (page 1136)

What are the units ofψ(x) ? Explain.

Short Answer

Expert verified

Hence, the unit is m-1/2

Step by step solution

01

Given information

ψ(x)

02

Explanation

We begin by recognising that probability is a dimensionless quantity, and that probability in the context of the wave function is:

P=|ψ(x)|2δx

Because the units of δx are (m), the units of |ψ(x)|2 must be m-1 in order to cancel the units of δx. As a result, ψ units are m-1/2.

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Most popular questions from this chapter

A particle is described by the wave function c1x2 = b cex/L x … 0 mm ce-x/L x Ú 0 mm where L = 2.0 mm.

a. Sketch graphs of both the wave function and the probability density as functions of x.

b. Determine the normalization constant c.

c. Calculate the probability of finding the particle within 1.0 mm of the origin. d. Interpret your answer to part b by shading the region representing this probability on the appropriate graph in part a

FIGURE Q39.1 shows the probability density for photons to be detected on thex-axis.

a. Is a photon more likely to be detected at x=0mor at x=1m ? Explain.

b. One million photons are detected. What is the expected number of photons in a 1−mm-wide interval at x=0.50m?

A 1.0-mm-diameter sphere bounces back and forth between two walls at x=0mmand x=100mm. The collisions are perfectly elastic, and the sphere repeats this motion over and over with no loss of speed. At a random instant of time, what is the probability that the center of the sphere is

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The probability density for finding a particle at position x is P1x2 = • a 11 - x2 -1 mm … x 6 0 mm b11 - x2 0 mm … x … 1 mm and zero elsewhere. a. You will learn in Chapter 40 that the wave function must be a continuous function. Assuming that to be the case, what can you conclude about the relationship between a and b? b. Determine values for a and b. c. Draw a graph of the probability density over the interval -2 mm … x … 2 mm. d. What is the probability that the particle will be found to the left of the origin?
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