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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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.
The normalization condition for a wavefunction Ψ(x, t) is given by
�
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Calculate the probability that an electron will be found (a) between x = 0.1 and 0.2 nm, (b) between 4.9 and 5.2 nm in a box of length L = 10 nm when its wavefunction is Ψ = (2/L)1/2 sin(2πx/L). Treat the wavefunction as a constant in the small region of interest and interpret δV as δx.
Chapter A Solutions
An Introduction to Thermal Physics
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