University Physics With Modern Physics Technology Update, Books A La Carte Edition
University Physics With Modern Physics Technology Update, Books A La Carte Edition
13th Edition
ISBN: 9780321898104
Author: Hugh D. Young, Roger A. Freedman
Publisher: Addison-wesley Longman
Question
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Chapter 41, Problem 1DQ
To determine

Compare the probability of finding the particle A described by the wave function ψ(x,y,z) and B described by the wave function ψ(x,y,z)eiϕ within a volume dV .

Expert Solution & Answer
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Answer to Problem 1DQ

The probability of finding the particle A described by the wave function ψ(x,y,z) is same as that of B described by the wave function ψ(x,y,z)eiϕ within a volume dV .

Explanation of Solution

Probability of finding the particle is known as probability density of the particle.

Write the expression for the probability density of the particle in volume dV

|ψ(x,y,z)|2dV=ψ*(x,y,z)ψ(x,y,z)dV (1)

Here,

ψ(x) is the wave function of particle.

dx is a small distance in x axis

Substitute ψ(x,y,z) in equation (1) to get probability of finding the particle A in volume dV .

PA=|ψ(x,y,z)|2dV=ψ*(x,y,z)ψ(x,y,z)dV

Here,

PA is the probability density of particle A in volume dV .

Substitute ψ(x,y,z)eiϕ in equation (1) to get probability of finding the particle A in volume dV .

PB=|ψ(x,y,z)eiϕ|2dV=(ψ(x,y,z)eiϕ)*(ψ(x,y,z)eiϕ)dV=ψ*(x,y,z)ψ(x,y,z)eiϕeiϕdV=ψ*(x,y,z)ψ(x,y,z)dV

Here,

PB is the probability density of particle B in volume dV .

Thus from above two calculation the probability of finding particle A in volume dV is same as that of B .

Conclusion:

Thus, the probability of finding the particle A described by the wave function ψ(x,y,z) is same as that of B described by the wave function ψ(x,y,z)eiϕ within a volume dV .

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Chapter 41 Solutions

University Physics With Modern Physics Technology Update, Books A La Carte Edition

Ch. 41 - Prob. 11DQCh. 41 - Prob. 12DQCh. 41 - Prob. 13DQCh. 41 - Prob. 14DQCh. 41 - Prob. 15DQCh. 41 - Prob. 16DQCh. 41 - Prob. 17DQCh. 41 - Prob. 18DQCh. 41 - Prob. 19DQCh. 41 - Prob. 20DQCh. 41 - Prob. 21DQCh. 41 - Prob. 22DQCh. 41 - Prob. 23DQCh. 41 - Prob. 1ECh. 41 - Prob. 2ECh. 41 - Prob. 3ECh. 41 - Prob. 4ECh. 41 - Prob. 5ECh. 41 - Prob. 6ECh. 41 - Prob. 7ECh. 41 - Prob. 8ECh. 41 - Prob. 9ECh. 41 - Prob. 10ECh. 41 - Prob. 11ECh. 41 - Prob. 12ECh. 41 - Prob. 13ECh. 41 - Prob. 14ECh. 41 - Prob. 15ECh. 41 - Prob. 16ECh. 41 - Prob. 17ECh. 41 - Prob. 18ECh. 41 - Prob. 19ECh. 41 - Prob. 20ECh. 41 - Prob. 21ECh. 41 - Prob. 22ECh. 41 - Prob. 23ECh. 41 - Prob. 24ECh. 41 - Prob. 25ECh. 41 - Prob. 26ECh. 41 - Prob. 27ECh. 41 - Prob. 28ECh. 41 - Prob. 29ECh. 41 - Prob. 30ECh. 41 - Prob. 31ECh. 41 - Prob. 32ECh. 41 - Prob. 33ECh. 41 - Prob. 34ECh. 41 - Prob. 35ECh. 41 - Prob. 36ECh. 41 - Prob. 37ECh. 41 - Prob. 38ECh. 41 - Prob. 39ECh. 41 - Prob. 40ECh. 41 - Prob. 41ECh. 41 - Prob. 42ECh. 41 - Prob. 43ECh. 41 - Prob. 44ECh. 41 - Prob. 45ECh. 41 - Prob. 46ECh. 41 - Prob. 47ECh. 41 - Prob. 48ECh. 41 - Prob. 49ECh. 41 - Prob. 50ECh. 41 - Prob. 51ECh. 41 - Prob. 52ECh. 41 - Prob. 53ECh. 41 - Prob. 54ECh. 41 - Prob. 55ECh. 41 - Prob. 56ECh. 41 - Prob. 57ECh. 41 - Prob. 58ECh. 41 - Prob. 59ECh. 41 - Prob. 60ECh. 41 - Prob. 61ECh. 41 - Prob. 62ECh. 41 - Prob. 63ECh. 41 - Prob. 64ECh. 41 - Prob. 65ECh. 41 - Prob. 66ECh. 41 - Prob. 67ECh. 41 - Prob. 68ECh. 41 - Prob. 69ECh. 41 - Prob. 70ECh. 41 - Prob. 71ECh. 41 - Prob. 72ECh. 41 - Prob. 73ECh. 41 - Prob. 74ECh. 41 - Prob. 75E
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