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Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-unhide:no; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman","serif";} </style> <![endif]--> <meta name=AUTHOR content="Lars Bergstrom"> <meta name=CREATED content="20080804;11300300"> <meta name=CHANGEDBY content="Lars Bergstrom"> <meta name=CHANGED content="20080804;11365500"> <!--[if gte mso 9]><xml> <o:shapedefaults v:ext="edit" spidmax="1026"/> </xml><![endif]--><!--[if gte mso 9]><xml> <o:shapelayout v:ext="edit"> <o:idmap v:ext="edit" data="1"/> </o:shapelayout></xml><![endif]--> </head> <body bgcolor="#FFFFCC" lang=SV link=blue vlink=purple style='tab-interval: 65.2pt'> <div class=WordSection1> <p style='margin-bottom:12.0pt'><span lang=EN-US style='mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0 width=665 style='width:498.75pt;mso-cellspacing:0cm;mso-yfti-tbllook:1184;mso-padding-alt: 0cm 0cm 0cm 0cm'> <COL WIDTH=665> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes;mso-yfti-lastrow:yes'> <td width=665 style='width:498.75pt;padding:0cm 0cm 0cm 0cm'> <h1 style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span class=SpellE><b><span lang=EN-US style='font-size:32.0pt;mso-fareast-font-family: "Times New Roman";color:#000099;mso-font-kerning:18.0pt;mso-ansi-language: EN-US'>Fysikum</span></b></span><b><span lang=EN-US style='font-size:24.0pt; mso-fareast-font-family:"Times New Roman";mso-font-kerning:18.0pt;mso-ansi-language: EN-US'><o:p></o:p></span></b></h1> <p style='margin-bottom:14.4pt'><span class=SpellE><span lang=EN-US style='font-size:18.0pt;color:#000099;mso-ansi-language:EN-US'>Stockholms</span></span><span lang=EN-US style='font-size:18.0pt;color:#000099;mso-ansi-language:EN-US'> <span class=SpellE>universitet</span></span><span lang=EN-US style='mso-ansi-language: EN-US'><o:p></o:p></span></p> <h1 align=center style='text-align:center'><b><span lang=EN-US style='font-size:32.0pt;mso-fareast-font-family:"Times New Roman";color:#000099; mso-font-kerning:18.0pt;mso-ansi-language:EN-US'>Quantum Mechanics III, 2011</span></b><b><span lang=EN-US style='font-size:24.0pt;mso-fareast-font-family:"Times New Roman"; mso-font-kerning:18.0pt;mso-ansi-language:EN-US'><o:p></o:p></span></b></h1> <p align=center style='margin-bottom:14.4pt;text-align:center'><i><span lang=EN-US style='mso-ansi-language:EN-US'>(Last updated&nbsp; 120116)<o:p></o:p></span></i></p> <div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt; padding:0cm 0cm 1.0pt 0cm'> <p align=center style='margin-bottom:14.4pt;text-align:center;border:none; mso-border-bottom-alt:solid windowtext 1.5pt;padding:0cm;mso-padding-alt: 0cm 0cm 1.0pt 0cm'><b style='mso-bidi-font-weight:normal'><span lang=EN-US style='font-size:14.0pt;color:#002060;mso-ansi-language:EN-US;mso-bidi-font-style: italic'>The course started Monday, October 31, at 10:15 in room FB41 and is now finished<o:p></o:p></span></b></p> <p align=center style='margin-bottom:14.4pt;text-align:center;border:none; mso-border-bottom-alt:solid windowtext 1.5pt;padding:0cm;mso-padding-alt: 0cm 0cm 1.0pt 0cm'><b style='mso-bidi-font-weight:normal'><span lang=EN-US style='font-size:14.0pt;color:#002060;mso-ansi-language:EN-US;mso-bidi-font-style: italic'><o:p>&nbsp;</o:p></span></b></p> </div> <p style='margin-bottom:14.4pt'><b style='mso-bidi-font-weight:normal'><span lang=EN-US style='font-size:14.0pt;color:#C00000;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></b></p> <p style='margin-bottom:13.7pt'><span style='font-family:Symbol'>·</span><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;</span><span lang=EN-US style='font-size:13.5pt;mso-ansi-language:EN-US'>There will be exercise sessions. There will be <a href="http://www.physto.se/~aschm/kvanttre.htm">a link to these.</a></span><span lang=EN-US style='mso-ansi-language:EN-US'> </span><span lang=EN-US style='font-size:13.5pt;mso-ansi-language:EN-US'>The detailed plan will appear when the course has started.<o:p></o:p></span></p> <p style='margin-bottom:13.7pt'><span style='font-family:Symbol'>·</span><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;</span><span lang=EN-US style='font-size:14.0pt;mso-ansi-language:EN-US'>The (preliminary) schedule for the course can be found <a href="qm/Timplan-11.htm">here</a>. <b style='mso-bidi-font-weight:normal'><span style='color:red'>New! Lecture notes (handwritten, and not always readable& ) in <span class=SpellE>pdf</span> format <a href="qm/pdfnotes.htm">here</a>.<o:p></o:p></span></b></span></p> <p style='margin-top:5.0pt;margin-right:0cm;margin-bottom:14.4pt;margin-left: 18.0pt;text-indent:-18.0pt'><span style='font-family:Symbol'>·</span><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;</span><span lang=EN-US style='font-size:13.5pt;mso-ansi-language:EN-US'>Home exercises will be announced on this page successively.</span><span lang=EN-US style='mso-ansi-language: EN-US'><o:p></o:p></span></p> <p style='margin-bottom:13.7pt'><span style='font-family:Symbol'>·</span><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;</span><span lang=EN-US style='font-size:13.5pt;mso-ansi-language:EN-US'>There are some notes</span><span lang=EN-US style='mso-ansi-language:EN-US'> </span><span lang=EN-US style='font-size:13.5pt;mso-ansi-language:EN-US'>about the importance of various sections of the <span style='color:red'><a href="http://www.physto.se/~lbe/qm/anvisningar_2011.htm">previous edition</a> </span>of the course book (<i style='mso-bidi-font-style:normal'>Sakurai, Modern Quantum Mechanics</i>). (Here is the version for the <span style='color:red'><a href="http://www.physto.se/~lbe/qm/anvisningar_sn_2011.htm">new edition</a> </span>of the book, <i style='mso-bidi-font-style:normal'>Sakurai and Napolitano, Modern Quantum Mechanics</i>.) This gives a rather good view of the requirements of the course. (For a formal summary of  <span class=SpellE>Betygskriterier</span> , in Swedish, click <a href="http://www.physto.se/%7Elbe/qm/betygskriterier.html">here</a>.)</span><span lang=EN-US style='mso-ansi-language:EN-US'><o:p></o:p></span></p> <p style='margin-bottom:13.7pt'><span style='font-family:Symbol'>·</span><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;</span><span lang=EN-US style='font-size:13.5pt;mso-ansi-language:EN-US'>In the later parts of the course, a sheet of <a href="http://www.physto.se/%7Elbe/qm/clebsch.pdf"><span class=SpellE>Clebsch-Gordan</span></a></span><a href="http://www.physto.se/%7Elbe/qm/clebsch.pdf"><span style='mso-ansi-language: EN-US'> </span><span lang=EN-US style='font-size:13.5pt;mso-ansi-language: EN-US'>coefficients</span></a><span style='mso-ansi-language:EN-US'> </span><span lang=EN-US style='font-size:13.5pt;mso-ansi-language:EN-US'>(from pdg.lbl.gov) may turn out to be useful. This may also be used at the written exam.</span><span lang=EN-US style='mso-ansi-language:EN-US'><o:p></o:p></span></p> <p style='margin-bottom:14.4pt'><b><span lang=EN-US style='font-size:13.5pt; mso-ansi-language:EN-US'>Purpose of the course:</span></b><span lang=EN-US style='mso-ansi-language:EN-US'><o:p></o:p></span></p> <p style='margin-top:5.0pt;margin-right:30.25pt;margin-bottom:14.4pt; margin-left:30.25pt'><span lang=EN-US style='font-size:13.5pt;mso-ansi-language: EN-US'>The purpose of this course is to give deepened knowledge of non-relativistic quantum mechanics. We will both give extended knowledge of concepts like symmetry transformations, and study phenomena like the interaction between radiation and matter. A brief introduction to quantum information will also be given.</span><span lang=EN-US style='mso-ansi-language: EN-US'><o:p></o:p></span></p> <p style='margin-top:5.0pt;margin-right:30.25pt;margin-bottom:14.4pt; margin-left:30.25pt'><span lang=EN-US style='font-size:13.5pt;mso-ansi-language: EN-US'>As the course develops, we will also encounter new concepts and new mathematical methods such as the path integral formulation of Feynman of quantum mechanics and the representation theory of the rotation group. Perturbation theory will also be introduced, both in its time independent and time dependent forms.</span><span lang=EN-US style='mso-ansi-language:EN-US'><o:p></o:p></span></p> <p style='margin-bottom:14.4pt'><b><span lang=EN-US style='font-size:13.5pt; mso-ansi-language:EN-US'>General information:</span></b><span lang=EN-US style='mso-ansi-language:EN-US'><o:p></o:p></span></p> <p style='margin-top:5.0pt;margin-right:0cm;margin-bottom:14.4pt;margin-left: 28.1pt'><span lang=EN-US style='font-size:13.5pt;mso-ansi-language:EN-US'>Teaching of the course will be done in 15 two-hour periods, with lectures given by Lars Bergström, and 7 exercise sessions led by <a href="mailto:angnis.schmidt-may@fysik.su.se"><span class=SpellE>Angnis</span> Schmidt-May</a>. The lectures are only meant as a <b style='mso-bidi-font-weight: normal'>complement</b> to the Sakurai-Robinson book, in particular explaining the more difficult parts, and will also include some extra material and newer developments. The course is defined by chapters 1 5 of Sakurai-Robinson, and extra distributed material. <o:p></o:p></span></p> <p style='margin-top:5.0pt;margin-right:0cm;margin-bottom:14.4pt;margin-left: 28.1pt'><b style='mso-bidi-font-weight:normal'><span lang=EN-US style='font-size:13.5pt;mso-ansi-language:EN-US'>There will be half a dozen home exercises, which are part of the course and will be important for the grading of the course in the following way: For each correctly solved set of home exercises, you will get 1 point, thus maximally 6 points in total. The sum will be divided by 2, rounded upwards to two significant digits, and added to the score of the written exam, which consists of 5 problems, each worth 3 points. Example: Suppose you get 4.5 points in the home exercises and solve correctly 4 of the problems in the exam. Then the total score will be 4.5/2 + 3 x 4 = 14.3 points. The scale of grades will approximately (but not strictly) follow the percentage scale of the  <span class=SpellE>Betygskriterier</span> mentioned above, thus in this case 14.3 = 0.79 x 18 (maximal number of points), which would give a  C grade (since it is in the interval 70  84%).<o:p></o:p></span></b></p> <p style='margin-top:5.0pt;margin-right:0cm;margin-bottom:14.4pt;margin-left: 28.1pt'><b style='mso-bidi-font-weight:normal'><span lang=EN-US style='font-size:13.5pt;mso-ansi-language:EN-US'>The points gathered at home exercises can only be used at the first exam, and at the first spare exam. After that, a new set has to be solved in the course the following year.<o:p></o:p></span></b></p> <p style='margin-top:5.0pt;margin-right:30.25pt;margin-bottom:14.4pt; margin-left:30.25pt'><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p style='margin-bottom:14.4pt'><b><span lang=EN-US style='font-size:13.5pt; mso-ansi-language:EN-US'>Home exercises (will appear here successively):</span></b><span lang=EN-US style='mso-ansi-language:EN-US'><o:p></o:p></span></p> <p style='margin-top:5.0pt;margin-right:0cm;margin-bottom:13.7pt;margin-left: 36.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo2;tab-stops:list 36.0pt'><![if !supportLists]><span style='font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:Symbol; mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><a href="http://www.physto.se/~lbe/qm/hu1_11.pdf"><span lang=EN-US style='font-size:13.5pt;mso-ansi-language:EN-US'>Set 1</span></a></p> <p style='margin-top:5.0pt;margin-right:0cm;margin-bottom:13.7pt;margin-left: 36.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo2;tab-stops:list 36.0pt'><![if !supportLists]><span style='font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:Symbol; mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><a href="http://www.physto.se/~lbe/qm/hu2_11.pdf"><span lang=EN-US style='font-size:13.5pt;mso-ansi-language:EN-US'>Set 2</span></a></p> <p style='margin-top:5.0pt;margin-right:0cm;margin-bottom:13.7pt;margin-left: 36.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo2;tab-stops:list 36.0pt'><![if !supportLists]><span style='font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:Symbol; mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><a href="http://www.physto.se/~lbe/qm/hu3_11.pdf"><span lang=EN-US style='font-size:13.5pt;mso-ansi-language:EN-US'>Set 3</span></a></p> <p style='margin-top:5.0pt;margin-right:0cm;margin-bottom:13.7pt;margin-left: 36.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo2;tab-stops:list 36.0pt'><![if !supportLists]><span style='font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:Symbol; mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><a href="http://www.physto.se/~lbe/qm/hu4_11.pdf"><span lang=EN-US style='font-size:13.5pt;mso-ansi-language:EN-US'>Set 4</span></a></p> <p style='margin-top:5.0pt;margin-right:0cm;margin-bottom:13.7pt;margin-left: 36.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo2;tab-stops:list 36.0pt'><![if !supportLists]><span style='font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:Symbol; mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><a href="http://www.physto.se/~lbe/qm/hu5_11.pdf"><span lang=EN-US style='font-size:13.5pt;mso-ansi-language:EN-US'>Set 5</span></a></p> <p style='margin-top:5.0pt;margin-right:0cm;margin-bottom:13.7pt;margin-left: 36.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo2;tab-stops:list 36.0pt'><![if !supportLists]><span style='font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:Symbol; mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:13.5pt; mso-ansi-language:EN-US'><a href="http://www.physto.se/~lbe/qm/hu6_11.pdf">Set 6</a></span></p> <p style='margin-top:5.0pt;margin-right:0cm;margin-bottom:13.7pt;margin-left: 36.0pt'><o:p>&nbsp;</o:p></p> <p style='margin-bottom:14.4pt'><b><span lang=EN-US style='font-size:13.5pt; mso-ansi-language:EN-US'>Literature</span></b><span lang=EN-US style='font-size:13.5pt;mso-ansi-language:EN-US'>: </span></p> <p style='margin-bottom:14.4pt'><span lang=EN-US style='font-size:13.5pt; mso-ansi-language:EN-US'>J.J. Sakurai and J. Napolitano: Modern Quantum Mechanics, Second Edition, Pearson 2011, ISBN-10: 0-321-50336-8; ISBN-13: 978-0-321-50336-7<o:p></o:p></span></p> <p style='margin-bottom:14.4pt'><span lang=EN-US style='font-size:13.5pt; mso-ansi-language:EN-US'>(<span style='color:red'>Previous edition: </span>J.J. Sakurai, Modern Quantum Mechanics, <span class=GramE>Addison</span>-Wesley ISBN-10: 0-201-53929-2, still covers most of the course).</span><span lang=EN-US style='mso-ansi-language:EN-US'><o:p></o:p></span></p> <p style='margin-bottom:14.4pt'><span lang=EN-US style='font-size:13.5pt; mso-ansi-language:EN-US'>A.S. <span class=SpellE>Abers</span>:&nbsp; Quantum <span class=SpellE>Mechnics</span> (Pearson 2003, ISBN 0-13-146100-1)</span><span lang=EN-US style='mso-ansi-language:EN-US'><o:p></o:p></span></p> <p style='margin-bottom:13.7pt'><span lang=EN-US style='font-size:13.5pt; mso-ansi-language:EN-US'>P. <span class=SpellE>Saltsidis</span> and B. <span class=SpellE>Brinne</span>: <a href="http://www.physto.se/%7Elbe/qm/pqm.pdf">Solutions to Problems in Quantum Mechanics, <span class=SpellE>pdf</span></a></span><span lang=EN-US style='mso-ansi-language:EN-US'><o:p></o:p></span></p> <p style='margin-bottom:14.4pt'><span lang=EN-US style='font-size:13.5pt; mso-ansi-language:EN-US'>Notes by T.H. Hansson on </span><a href="http://www.physto.se/~lbe/qm/cstates.pdf"><span lang=EN-US style='font-size:13.5pt;mso-ansi-language:EN-US'>Coherent states, <span class=SpellE>pdf</span></span></a><u><span lang=EN-US style='mso-ansi-language: EN-US'>&nbsp;</span></u><span lang=EN-US style='mso-ansi-language:EN-US'><o:p></o:p></span></p> <p style='margin-bottom:14.4pt'><span lang=EN-US style='font-size:13.5pt; mso-ansi-language:EN-US'>Notes by J. <span class=SpellE>Preskill</span> on </span><span style='font-size:13.5pt'><a href="http://www.physto.se/%7Elbe/qm/preskill.pdf"><span lang=EN-US style='mso-ansi-language:EN-US'>Quantum Information and Computing, <span class=SpellE>pdf</span></span></a></span><span lang=EN-US style='mso-ansi-language:EN-US'><o:p></o:p></span></p> <p style='margin-bottom:14.4pt'><span lang=EN-US style='mso-ansi-language: EN-US'>&nbsp;<i>The Compendium with solutions (<span class=SpellE>Brinne-Saltsidis</span>) can also be bought at the student expedition.</i> <br> &nbsp; <br> &nbsp;</span><b><span lang=EN-US style='font-size:13.5pt;mso-ansi-language: EN-US'>Old written exams (<span class=SpellE>pdf</span> files):</span></b><span lang=EN-US style='mso-ansi-language:EN-US'><o:p></o:p></span></p> <p style='margin-top:5.0pt;margin-right:0cm;margin-bottom:14.4pt;margin-left: 36.0pt;text-indent:-18.0pt;mso-list:l1 level1 lfo4'><![if !supportLists]><span lang=EN-US style='font-size:13.5pt;font-family:Symbol;mso-fareast-font-family: Symbol;mso-bidi-font-family:Symbol;mso-ansi-language:EN-US'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:13.5pt; mso-ansi-language:EN-US'><a href="qm/tenta09.pdf">2009 (with solutions)</a><o:p></o:p></span></p> <p style='margin-top:5.0pt;margin-right:0cm;margin-bottom:14.4pt;margin-left: 36.0pt;text-indent:-18.0pt;mso-list:l1 level1 lfo4'><![if !supportLists]><span lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol; mso-bidi-font-family:Symbol;mso-ansi-language:EN-US'><span style='mso-list: Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:13.5pt; mso-ansi-language:EN-US'><a href="qm/tenta_2010_1.pdf">2010 (with solutions)</a></span><span lang=EN-US style='font-family:Symbol;mso-ansi-language:EN-US'><o:p></o:p></span></p> <p style='margin-top:5.0pt;margin-right:0cm;margin-bottom:14.4pt;margin-left: 36.0pt;text-indent:-18.0pt;mso-list:l1 level1 lfo4'><![if !supportLists]><span lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol; mso-bidi-font-family:Symbol;mso-ansi-language:EN-US'><span style='mso-list: Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:13.5pt; mso-ansi-language:EN-US'><a href="qm/tenta_2011_1_sol.pdf">2011 (with solutions)</a></span><span lang=EN-US style='font-family:Symbol;mso-ansi-language: EN-US'><o:p></o:p></span></p> <p style='margin-top:5.0pt;margin-right:0cm;margin-bottom:14.4pt;margin-left: 36.0pt;text-indent:-18.0pt;mso-list:l1 level1 lfo4'><![if !supportLists]><span lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol; mso-bidi-font-family:Symbol;mso-ansi-language:EN-US'><span style='mso-list: Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:13.5pt; mso-ansi-language:EN-US'><a href="qm/tenta_2012_1_wsol.pdf">2012 (with solutions)</a></span><span lang=EN-US style='font-family:Symbol;mso-ansi-language: EN-US'><o:p></o:p></span></p> <p style='margin-top:5.0pt;margin-right:0cm;margin-bottom:14.4pt;margin-left: 36.0pt'><span lang=EN-US style='font-family:Symbol;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p style='margin-top:5.0pt;margin-right:0cm;margin-bottom:14.4pt;margin-left: 36.0pt'><span lang=EN-US style='font-family:Symbol;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p style='margin-bottom:14.4pt'><span lang=EN-US style='font-family:Symbol; mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p style='margin-bottom:14.4pt'><span lang=EN-US style='mso-ansi-language: EN-US'><o:p>&nbsp;</o:p></span></p> </td> </tr> </table> <p style='margin-bottom:0cm;margin-bottom:.0001pt'><span lang=EN-US style='mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> </div> </body> </html>