Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
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Chapter 7, Problem 2CQ
To determine
The reason for that degeneracies are accidental.
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The spherical harmonics are the eigenfunctions of ?̂2 and ?̂ ? for the rigid rotor and thehydrogen atom (and other spherically symmetric problems). In this problem, we willexamine the nature of the angular nodes for these systems.Since the spherical harmonics include a factor of eim, which never has magnitude zero, forthis exercise we will construct some linear combinations of the spherical harmonics so weare working with real-valued functions. Two of the real-valued spherical harmonics are:12 (?1−1 + ?11) = 12 √ 32? sin ? cos ? 12? (?32 − ?3−2) = 14 √1052? sin2 ? cos ? sin 2?(a) Determine the angles at which nodal surfaces will occur for each of these functions, anddescribe the nature of the nodal surfaces that they represent. In other words, identifythe locations of nodal planes and other surfaces in the Cartesian axis system.(b) What atomic orbitals (e.g. 1s, 2p, etc.) are represented by these functions and what isthe total number of distinct angular nodal surfaces?
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Chapter 7 Solutions
Modern Physics
Ch. 7 - Prob. 1CQCh. 7 - Prob. 2CQCh. 7 - Prob. 3CQCh. 7 - Prob. 4CQCh. 7 - Prob. 5CQCh. 7 - Prob. 6CQCh. 7 - Prob. 7CQCh. 7 - Prob. 8CQCh. 7 - Prob. 9CQCh. 7 - What are the dimensions of the spherical harmonics...
Ch. 7 - Prob. 11CQCh. 7 - Prob. 12CQCh. 7 - Prob. 13CQCh. 7 - Prob. 14CQCh. 7 - Prob. 15CQCh. 7 - Prob. 16CQCh. 7 - Prob. 17ECh. 7 - Prob. 18ECh. 7 - Prob. 19ECh. 7 - Prob. 20ECh. 7 - Prob. 21ECh. 7 - Prob. 22ECh. 7 - Prob. 23ECh. 7 - Prob. 24ECh. 7 - Prob. 25ECh. 7 - Prob. 26ECh. 7 - Prob. 27ECh. 7 - Show that of hydrogen’s spectral seriesLyman,...Ch. 7 - Prob. 29ECh. 7 - Prob. 30ECh. 7 - Prob. 31ECh. 7 - Prob. 32ECh. 7 - Prob. 33ECh. 7 - Prob. 34ECh. 7 - Prob. 35ECh. 7 - Prob. 36ECh. 7 - Prob. 37ECh. 7 - A particle orbiting due to an attractive central...Ch. 7 - Prob. 39ECh. 7 - Prob. 40ECh. 7 - Prob. 41ECh. 7 - Prob. 42ECh. 7 - Prob. 43ECh. 7 - How many different 3d states are there? What...Ch. 7 - Prob. 45ECh. 7 - Prob. 46ECh. 7 - Prob. 47ECh. 7 - Prob. 48ECh. 7 - Prob. 49ECh. 7 - Prob. 50ECh. 7 - Prob. 51ECh. 7 - Prob. 52ECh. 7 - Prob. 53ECh. 7 - Prob. 54ECh. 7 - For states where l=n1 , the radial probability...Ch. 7 - Prob. 56ECh. 7 - Prob. 57ECh. 7 - Prob. 58ECh. 7 - Prob. 59ECh. 7 - Prob. 60ECh. 7 - Prob. 61ECh. 7 - Prob. 62ECh. 7 - Prob. 63ECh. 7 - Prob. 64ECh. 7 - Prob. 65ECh. 7 - Prob. 66ECh. 7 - Prob. 67ECh. 7 - Prob. 68ECh. 7 - Prob. 69ECh. 7 - Prob. 70ECh. 7 - Prob. 71ECh. 7 - Prob. 72ECh. 7 - Prob. 73ECh. 7 - Prob. 74ECh. 7 - Prob. 75ECh. 7 - Prob. 76ECh. 7 - Prob. 77ECh. 7 - Prob. 78ECh. 7 - Prob. 79CECh. 7 - Prob. 80CECh. 7 - Prob. 81CECh. 7 - Prob. 83CECh. 7 - Prob. 84CECh. 7 - Prob. 85CECh. 7 - Prob. 86CECh. 7 - Prob. 87CECh. 7 - Prob. 89CE
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