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How do you know?\ \>", "Text", CellChangeTimes->{{3.54008523076204*^9, 3.5400852359793787`*^9}, { 3.733238008522544*^9, 3.733238015187915*^9}, {3.7348016222233334`*^9, 3.7348016279906635`*^9}, {3.735294452865024*^9, 3.7352945262024107`*^9}, { 3.7352945573242064`*^9, 3.73529458529208*^9}, 3.7352997728217154`*^9}, FontFamily->"Times New Roman", FontSize->24, Background->RGBColor[0.88, 1, 0.88]], Cell["\<\ 1b) Do the wavefunctions of the linear combinations of energy eigenstates \ \[CapitalPsi]T3 through and \[CapitalPsi]T11 have time dependence? How do you \ know?\ \>", "Text", CellChangeTimes->{{3.54008523076204*^9, 3.5400852359793787`*^9}, { 3.733238008522544*^9, 3.733238015187915*^9}, {3.7348016222233334`*^9, 3.7348016279906635`*^9}, {3.735294452865024*^9, 3.7352945262024107`*^9}, { 3.7352945573242064`*^9, 3.735294625869445*^9}, {3.735299775802947*^9, 3.7352997762511168`*^9}}, FontFamily->"Times New Roman", FontSize->24, Background->RGBColor[0.88, 1, 0.88]], Cell["", "Text", CellChangeTimes->{{3.5207900329256697`*^9, 3.520790039425545*^9}, { 3.5207905528063135`*^9, 3.52079057796208*^9}, {3.520790669257202*^9, 3.520790688522457*^9}, {3.520792276476343*^9, 3.5207922883979893`*^9}, 3.731802105804598*^9, {3.7332453910993633`*^9, 3.73324543146161*^9}, { 3.733245465591494*^9, 3.73324552648767*^9}, {3.7332457859000053`*^9, 3.7332458946366596`*^9}, {3.733246416026823*^9, 3.7332464976539507`*^9}, { 3.733409647622547*^9, 3.733409690789016*^9}, {3.7334097220978065`*^9, 3.7334098097328186`*^9}, {3.733409843957776*^9, 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Why or why not?\ \>", "Text", CellChangeTimes->{{3.54008523076204*^9, 3.5400852359793787`*^9}, { 3.733238008522544*^9, 3.733238015187915*^9}, {3.7348016222233334`*^9, 3.7348016279906635`*^9}, {3.735294452865024*^9, 3.7352945262024107`*^9}, { 3.7352945573242064`*^9, 3.73529458529208*^9}, {3.7352946557276373`*^9, 3.735294691462845*^9}, {3.735294758058416*^9, 3.735294760561442*^9}, { 3.735299779715212*^9, 3.735299779955201*^9}}, FontFamily->"Times New Roman", FontSize->24, Background->RGBColor[0.88, 1, 0.88]], Cell["\<\ 2b) Do the probability densities of the linear combinations of energy \ eigenstates \[CapitalPsi]T3 through and \[CapitalPsi]T11 have time \ dependence? Why or why not?\ \>", "Text", CellChangeTimes->{{3.54008523076204*^9, 3.5400852359793787`*^9}, { 3.733238008522544*^9, 3.733238015187915*^9}, {3.7348016222233334`*^9, 3.7348016279906635`*^9}, {3.735294452865024*^9, 3.7352945262024107`*^9}, { 3.7352945573242064`*^9, 3.735294625869445*^9}, {3.735294656950349*^9, 3.735294660382626*^9}, 3.735294694769579*^9, 3.735294764251378*^9, { 3.7352997816430273`*^9, 3.735299781898988*^9}}, FontFamily->"Times New Roman", FontSize->24, Background->RGBColor[0.88, 1, 0.88]], Cell["", "Text", CellChangeTimes->{{3.5207900329256697`*^9, 3.520790039425545*^9}, { 3.5207905528063135`*^9, 3.52079057796208*^9}, {3.520790669257202*^9, 3.520790688522457*^9}, {3.520792276476343*^9, 3.5207922883979893`*^9}, 3.731802105804598*^9, {3.7332453910993633`*^9, 3.73324543146161*^9}, { 3.733245465591494*^9, 3.73324552648767*^9}, {3.7332457859000053`*^9, 3.7332458946366596`*^9}, {3.733246416026823*^9, 3.7332464976539507`*^9}, { 3.733409647622547*^9, 3.733409690789016*^9}, 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In which direction do they rotate?\ \>", "Text", CellChangeTimes->{{3.54008523076204*^9, 3.5400852359793787`*^9}, { 3.733238008522544*^9, 3.733238015187915*^9}, {3.7348016222233334`*^9, 3.7348016279906635`*^9}, {3.735294452865024*^9, 3.7352945262024107`*^9}, { 3.7352945573242064`*^9, 3.735294625869445*^9}, {3.735294656950349*^9, 3.735294660382626*^9}, 3.735294694769579*^9, 3.735294764251378*^9, { 3.735299230219823*^9, 3.735299283348209*^9}, {3.735299785787365*^9, 3.735299787884906*^9}}, FontFamily->"Times New Roman", FontSize->24, Background->RGBColor[0.88, 1, 0.88]], Cell["3b) When do probability densities not rotate? Explain.", "Text", CellChangeTimes->{{3.54008523076204*^9, 3.5400852359793787`*^9}, { 3.733238008522544*^9, 3.733238015187915*^9}, {3.7348016222233334`*^9, 3.7348016279906635`*^9}, {3.735294452865024*^9, 3.7352945262024107`*^9}, { 3.7352945573242064`*^9, 3.735294625869445*^9}, {3.735294656950349*^9, 3.735294660382626*^9}, 3.735294694769579*^9, 3.735294764251378*^9, { 3.735299230219823*^9, 3.7352992845164003`*^9}, {3.735299789830587*^9, 3.7352997910153437`*^9}}, FontFamily->"Times New Roman", FontSize->24, Background->RGBColor[0.88, 1, 0.88]], Cell[TextData[{ "4) What is different between the ", StyleBox["equations", FontWeight->"Bold"], " for \[CapitalPsi]T3 through \[CapitalPsi]T6? 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