{"id":1029,"date":"2017-02-20T10:14:28","date_gmt":"2017-02-20T17:14:28","guid":{"rendered":"https:\/\/sites.evergreen.edu\/psam1617\/?p=1029"},"modified":"2017-02-20T21:10:27","modified_gmt":"2017-02-21T04:10:27","slug":"week-17-problem-sets-em6-la6-qm3","status":"publish","type":"post","link":"https:\/\/sites.evergreen.edu\/psam1617\/week-17-problem-sets-em6-la6-qm3\/","title":{"rendered":"Week 17 Problem Sets: EM#6, LA#6, QM#3"},"content":{"rendered":"<p>Problem Sets to be completed in your corresponding PSNs by noon Sun. Feb. 26.<\/p>\n<ul>\n<li>EM PS#6: Griffiths: 4.11&amp;4.17, 4.12, 4.15, 4.16(a), 4.20, 4.21, 4.33, 4.34, 4.35<\/li>\n<li>LA PS#6: Lay 5.5: 4&amp;6, 8&amp;12, 23, 24<\/li>\n<li>QM PS#3: Townsend: 3.8, 3.13, 3.15, 3.16, 3.17, 3.18, 3.20, 3.22, 3.24, 3.25<\/li>\n<\/ul>\n<ul>\n<li>EM notes: For 4.12, note that since the polarization is uniform, the P and dot product can be pulled out in front of the integral; the integral is now a modified version of an integral you carried out in the collected set of problem 2.7, problem 2.8, Example 2.3 and problem 2.12. For 4.34, you&#8217;ll get to show that the information in the problem statement means that the dielectric constant is given by 1+ <em>x\/d<\/em>. For 4.35, you&#8217;ll get to use the Dirac delta function.<\/li>\n<li>LA notes: Lay uses the overbar to mean complex conjugate (recall that Townsend uses *), such that <span style=\"text-decoration: overline\">A<\/span> = A*. For 4 and 6, follow the approach outlined in Example 2. For 8 and 12, use Example 6 (as directed). Problems 23 and 24 are related to what you did for the last problem on LA\/QM Exam 1; some of you might be interested in seeing what happens if you replace the condition that <em>A<\/em> is an <em>n<\/em> x <em>n<\/em> real matrix with the property <em>A<sup>T<\/sup> = A<\/em> with the condition that <em>A<\/em> is an <em>n<\/em> x <em>n<\/em> complex matrix with the property that<em> <span style=\"text-decoration: overline\">A<\/span><sup>T<\/sup> = A<\/em> (in other words, <em>A<\/em> is Hermitian), in which case this might become an alternative proof that the eigenvalues of a Hermitian matrix operator are real.<\/li>\n<li>QM notes: Problem 3.8 should be straightforward. For 3.24, choose the simplest <em>N<\/em> (e.g. with phase = 0). I plan to go over 3.2, 3.9, 3.10, 3.11, 3.12, 3.14, parts of 3.15 and 3.18, and 3.21 in class, which should hopefully prepare you for the rest of the assignment.\u00a0<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Problem Sets to be completed in your corresponding PSNs by noon Sun. Feb. 26. EM PS#6: Griffiths: 4.11&amp;4.17, 4.12, 4.15, 4.16(a), 4.20, 4.21, 4.33, 4.34, 4.35 LA PS#6: Lay 5.5: 4&amp;6, 8&amp;12, 23, 24 QM PS#3: Townsend: 3.8, 3.13, 3.15, &hellip; <a href=\"https:\/\/sites.evergreen.edu\/psam1617\/week-17-problem-sets-em6-la6-qm3\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":219,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/sites.evergreen.edu\/psam1617\/wp-json\/wp\/v2\/posts\/1029"}],"collection":[{"href":"https:\/\/sites.evergreen.edu\/psam1617\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.evergreen.edu\/psam1617\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.evergreen.edu\/psam1617\/wp-json\/wp\/v2\/users\/219"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.evergreen.edu\/psam1617\/wp-json\/wp\/v2\/comments?post=1029"}],"version-history":[{"count":0,"href":"https:\/\/sites.evergreen.edu\/psam1617\/wp-json\/wp\/v2\/posts\/1029\/revisions"}],"wp:attachment":[{"href":"https:\/\/sites.evergreen.edu\/psam1617\/wp-json\/wp\/v2\/media?parent=1029"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.evergreen.edu\/psam1617\/wp-json\/wp\/v2\/categories?post=1029"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.evergreen.edu\/psam1617\/wp-json\/wp\/v2\/tags?post=1029"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}