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A definite-momentum wave function can be expressed by the

An Introduction to Thermal Physics | 1st Edition | ISBN: 9780201380279 | Authors: Daniel V. Schroeder ISBN: 9780201380279 40

Solution for problem 8P Chapter A

An Introduction to Thermal Physics | 1st Edition

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An Introduction to Thermal Physics | 1st Edition | ISBN: 9780201380279 | Authors: Daniel V. Schroeder

An Introduction to Thermal Physics | 1st Edition

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Problem 8P

Problem 8P

A definite-momentum wave function can be expressed by the formula Ψ (x) = A(cos kx +i sin kx), where A and k are constants.

(a) How is the constant k related to the particle’s momentum? (Justify your answer.)

(b) Show that, if a particle has such a wavefunction, you are equally likely to find it at any position x.

(c) Explain why the constant A must be infinitesimal, if this formula is to be valid for all x.

(d) Show that this wave function satisfies the differential equation /dx = ikΨ.

(e) Often the function cosθ + i sinθ is written instead as eiθ. Treating the i as an ordinary constant. show that the function. A eikx obeys the same differential equation as in part (d).

Step-by-Step Solution:

Problem 8P

Solution 8P

Step 1 :

Introduction :

In this question, we need to show a relation between constant k and momentum p

In the second part , we need to show, for the given wave function, the particle can be found at any  x position

In the third part, we need to explain the reason for constant A to be infinitesimal for the formula to be valid for values of x  

In the fourth part, we need to differentiate the given wave function to obtain

And finally, we need to show function obeys same differential equation and yields , if

is written as

Given wave function

Step 2 of 6

Chapter A, Problem 8P is Solved
Step 3 of 6

Textbook: An Introduction to Thermal Physics
Edition: 1
Author: Daniel V. Schroeder
ISBN: 9780201380279

The full step-by-step solution to problem: 8P from chapter: A was answered by , our top Physics solution expert on 07/05/17, 04:29AM. This textbook survival guide was created for the textbook: An Introduction to Thermal Physics , edition: 1. An Introduction to Thermal Physics was written by and is associated to the ISBN: 9780201380279. This full solution covers the following key subjects: function, constant, show, Differential, sin. This expansive textbook survival guide covers 10 chapters, and 454 solutions. The answer to “A definite-momentum wave function can be expressed by the formula ? (x) = A(cos kx +i sin kx), where A and k are constants.(a) How is the constant k related to the particle’s momentum? (Justify your answer.)________________(b) Show that, if a particle has such a wavefunction, you are equally likely to find it at any position x.________________(c) Explain why the constant A must be infinitesimal, if this formula is to be valid for all x.________________(d) Show that this wave function satisfies the differential equation d?/dx = ik?.________________(e) Often the function cos? + i sin? is written instead as ei?. Treating the i as an ordinary constant. show that the function. A eikx obeys the same differential equation as in part (d).” is broken down into a number of easy to follow steps, and 121 words. Since the solution to 8P from A chapter was answered, more than 302 students have viewed the full step-by-step answer.

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A definite-momentum wave function can be expressed by the