/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q21P The following problem arises in ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 15: Q21P (page 744)

The following problem arises in quantum mechanics (see Chapter 13, Problem7.21). Find the number of ordered triples of nonnegative integers a, b, c whose suma+b+c is a given positive integer n. (For example, ifn=2, we could have(a,b,c)=(2,0,0)or(2,0,2)or (0,0,2)or (0,1,1)or or (1,0,1)or (1,1,0).) Hint: Show that this is the same as the number of distinguishable distributions of n identical balls in3boxes, and follow the method of the diagram in Example 5.

Short Answer

Expert verified

The required value is given below.

M=C(n+2,n)

Step by step solution

01

Given Information

Non negative integers whose sum is a+b+c.

02

Definition of uniform sample spaces

If a given experiment's sample space is known to be uniform, the probability of an event can be calculated using the event sizes and the sample space.

03

Find the values

Let the sum be n=a+b+c.

Bose-Einstein techniques in distribution is given below.

M=C(R鈭�1+K,K)

Where K is number of balls or total sum of variable.

R is the number of variable or number of boxes.

M=C(3鈭�1+n,n)=C(n+2,n)

Hence the required value is mentioned below.

M=C(n+2,n)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Use the sample space of Example 1 above, or one or more of your sample spaces in Problem 11, to answer the following questions.

(a) If there were more heads than tails, what is the probability of one tail?

(b) If two heads did not appear in succession, what is the probability of all tails?

(c) If the coins did not all fall alike, what is the probability that two in succession

were alike?

(d) If Nt=numberoftailsand Nh=numberofheads, what is the probability

That |Nh-Nt|=1?

(e) If there was at least one head, what is the probability of exactly two heads?

Let x1,x2,..,xnbe independent random variables, each with density function f(x), expected value渭 , and variance蟽2 . Define the sample meanby.x鈭�=鈭�i=1nxiShowthatE(x鈭�)=渭,and .var(x鈭�)=蟽2n (See Problems 5.9,5.13and6.15.)

Set up an appropriate sample space for each of Problems 1.1 to 1.10 and use itto solve the problem. Use either a uniform or non-uniform sample space or try both.

You are trying to find instrument A in a laboratory. Unfortunately, someone has put both instruments A and another kind (which we shall call B) away in identical unmarked boxes mixed at random on a shelf. You know that the laboratory has 3 A鈥檚 and 7 B鈥檚. If you take down one box, what is the probability that you get an A? If it is a B and you put it on the table and take down another box, what is the probability that you get an A this time?

A card is selected from a shuffled deck. What is the probability that it is either a king or a club? That it is both a king and a club?

(a) Following the methods of Examples 3,4,5, show that the number of equally likely ways of putting N particles in n boxes,n>N, nNisfor Maxwell Boltzmann particles, C(n,N)for Fermi-Dirac particles, C(n鈭�1+N,N)andfor Bose-Einstein particles.

(b) Show that if n is much larger than N (think, for example, ofn=106,N=10), then both the Bose-Einstein and the Fermi-Dirac results in part (a) contain products of N numbers, each number approximately equal to n. Thus show that for n N, both the BE and the FD results are approximately equal tonNN!which is1N!times the MB result.
See all solutions

Recommended explanations on Physics Textbooks

Force

Read Explanation

Physics of Motion

Read Explanation

Electrostatics

Read Explanation

Turning Points in Physics

Read Explanation

Wave Optics

Read Explanation

Physical Quantities And Units

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.