An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Question
Chapter A.2, Problem 8P
(a)
To determine
The relation between constant k to the particles momentum.
(b)
To determine
To Show:If a particle has such wave function then it is equally likely to find the particle at any position.
(c)
To determine
To Explain: The constant A must be infinitesimal if this formula is to be valid for all
(d)
To determine
To Show: The given wave function satisfies the differential equation
(e)
To determine
To show: the function
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The normalization condition for a wavefunction Ψ(x, t) is given by
�
∞
−∞
Ψ∗(x, t)Ψ(x, t)dx = 1.
This necessarily means that the LHS has to be independent of time. Show
that this is indeed the case
A definite-momentum wavefunction can be expressed by the formula W(x) = A (cos kx +i sin kx), where A and k are constants.
How is the constant k related to the particle's momentum? (Justify your answer.)
An observable, q, is represented by an operator, . Assuming a system is in a state Ψ(x,t). a) Write an expression for the expectation value of the observable,<q>. b) Write an expression for the uncertainty in measuring the observable, ∆q. c) Write expressions for the operators relating to position and momentum ( and ) and for the squares of these operators. d) If Ψ(x,t) is an eigenstate of , write an equation relating the eigenvalue and itsoperator.
Chapter A Solutions
An Introduction to Thermal Physics
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