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classes_winter09_113AID28_P_21_113A_W09

classes_winter09_113AID28_P_21_113A_W09 - system...

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Preview #21 (Chem113A W’09, due Mon. 2/23/09 at 12:05pm in class) Assigned reading: Engel 7.2—7.3 Attendance record : I am [ ] present at or [ ] absent from this class meeting (see date and time above). Name: ________________________ Forming study groups is permissible, but you must construct your solutions independently. By writing down my name, I confirm that I strictly obey the academic ethic code when doing this preview and my statement on attendance (above) is correct. Please write down the names of everyone who you worked with on this preview in the space above. [1] “Particle on a ring” and “particle on a sphere” (Remarks: We studied quantum SHO by Schrodinger’s conventional approach and Dirac’s elegant approach, and then applied it to understand/predict vibrational spectroscopy. We now move on to study a new quantum
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Unformatted text preview: system: “particle on a ring”/”particle on a sphere” by Schrodinger’s approach and Dirac’s algebra. Later, we will apply it to understand/predict rotational spectroscopy.) The time-independent Schrodinger equation (in the spherical coordinate system) for the rotational motion of a diatomic molecule such as I 2 is shown in Engel Eq. (7.17). This is also the TISE for a particle on a sphere. [1](a) Please prove by algebra that the spherical harmonics function Y 1,+1 (i.e., l quantum number =1, m quantum number =+1) is indeed a solution to Eq. (7.17). [1](b) What is the corresponding eigenvalue E? [Hint: Plug the functional form of Y 1,+1 into Eq. (7.17) and show LHS=RHS. You can find the functional form of Y 1,+1 on p. 116 of Engel’s and the correct answers for E in Eq. (7.26)]...
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