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 timeindependent 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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 Winter '07
 Lin
 Electron, Quantum Chemistry, Schrodinger Equation, Spherical coordinate system, timeindependent Schrodinger equation, academic ethic code

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