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Unformatted text preview: Consider the hydrogen atom (ignoring the spin-orbit interaction), with eigen-functions given by the chart on page 243 of your textbook. 1. For a given eigenfunction nlm , what is the energy? 2. Consider the r dependence: (a) Find the expectation value of r for the n = 1 , l = 0 state by explicit calculation. Check units. (b) Do you expect the expectation value of r for, say, the n = 2 , l = 0 state to be bigger or smaller? Why? 3. Suppose we had singly ionized helium (2 protons and 2 neutrons in the nucleus, one electron) instead of hydrogen. (a) By what factor would the energy levels E n change with respect to hydrogen? (b) By what factor would the fractional energy spacing E n +1-E n E n change with respect to hydrogen? 1...
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- Spring '09