Tutorials in Introductory Physics
1st Edition
ISBN: 9780130970695
Author: Peter S. Shaffer, Lillian C. McDermott
Publisher: Addison Wesley
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Chapter 23.1, Problem 3eTH
(i)
To determine
The pulse at 0.3 s.
(ii)
To determine
Inconsistency with the free-end boundary condition for the given pulse.
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Consider the waveforms given below
1. Determine the dimensionality of the waveforms and a set of basis functions.
2. Use the basis functions to represent the four waveforms by vectors s1, s2,
S3, S4.
3. Determine the minimum distance between any pair of vectors.
s3() |
- 2
2
-3
2.
|m|
1. Write the general equation for the spherical harmonic Y; (0, p) and identify Om(), P' (cos 0), and the
normalization constant.
2. Show that Y, (0, $) is an eigenfunction of L². What is the eigenvalue?
3. Show that Y (0,¢) and Y†'(0, p) are orthogonal.
4.
State the relation of the reciprocal basis vectors to the direct basis vectors to obtain the
G.T = 2nn. Show G.T = 2n and what does means by this equation?
st
5. Sketch the first Brillouin Zone ( 1 BZ) for a 2D square of real lattice with a = b= 2Ă.
Draw the incident wave vector, Ko, scattered wave vector, K and vector G at boundary
st
of the 1 BZ to show the (0, -1) is the valid lattice point for constructive interference.
st
State the range of the 1 BZ for both sides, which is along the direction of a*(kx axis )
and b* (ky axis), respectively.
6. Draw a 2D square reciprocal lattice and identify the 1st and 2nd Brillouin zones.
Apply the Laue condition by drawing relevant vectors in the reciprocal lattice
diagram to show that the (1, -1) is a valid reciprocal lattice point.
Chapter 23 Solutions
Tutorials in Introductory Physics
Ch. 23.1 - Prob. 1THCh. 23.1 - In the spaces provided belowright, carefully draw...Ch. 23.1 - Prob. 2bTHCh. 23.1 - We begin by considering the forces exerted on a...Ch. 23.1 - Prob. 3bTHCh. 23.1 - Prob. 3cTHCh. 23.1 - Prob. 3dTHCh. 23.1 - Prob. 3eTHCh. 23.1 - Prob. 4THCh. 23.2 - Prob. 1TH
Ch. 23.2 - Prob. 2aTHCh. 23.2 - Prob. 2bTHCh. 23.2 - Prob. 2cTHCh. 23.2 - Prob. 3aTHCh. 23.2 - Prob. 3bTHCh. 23.2 - Prob. 3cTHCh. 23.2 - The figure at right has several errors. How many...Ch. 23.3 - Prob. 1aTHCh. 23.3 - Prob. 1bTHCh. 23.3 - Prob. 1cTHCh. 23.3 - For each of the periodic functions below, indicate...Ch. 23.3 - Prob. 2THCh. 23.3 - Use trigonometry to determine the mathematical...Ch. 23.3 - Starting from the equation that you wrote above,...Ch. 23.3 - Suppose the speed of the refracted wave were half...Ch. 23.3 - Prob. 3dTHCh. 23.4 - A long, thin steel wire is cut in half, and each...Ch. 23.4 - A long, thin steel wire is cut in half, and each...Ch. 23.4 - A long, thin steel wire is cut in half, and each...Ch. 23.4 - Consider an instant when the fields are nonzero at...Ch. 23.4 - How would your answers to parta be different if...Ch. 23.4 - Prob. 3TH
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