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Unformatted text preview: Physical Chemistry Course Number: C362 12.2 The hydrogen atom Schrodinger Equation in spherical coordinates 1. As noted in the spherical coordinates handout it is always convenient to choose a coordinate system that represents the symmetry of the problem. In this case, again, there is an inherent spherical symmetry that is enforced by the potential. What is meant by this statement is that as the electron moves on the surface of a sphere of any radius, with the nucleus at the center of the sphere, it feels the same potential all through since the potential energy is only a function of | r e N | . This is called spherical symmetry!! 2. In general, we should note that the symmetry of the problem is that enforced by the potential energy function and the subject of group theory is based on exploiting such symmetries to simplify problems of quantum mechanics and in many cases obtain accurate qualitative results without doing much of algebra! 3. Back to Eq. ( 12.23 ) we need to write 2 r e- N in spherical coordinates. Using the results in the spherical coordiantes handout (please go over it), we obtain: 2 = 1 r 2 sin braceleftBigg r bracketleftBigg r 2 sin r bracketrightBigg + bracketleftBigg sin bracketrightBigg + bracketleftBigg...
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- Winter '11
- 2 L, Schr¨ dinger equation, Srinivasan S. Iyengar