Absorption and Superposition States in Hydrogen Atoms

Now imagine that the electric field were instantaneously turned off. The electronic cloud is distorted from the lowest energy state S = 0, so there will be a restoring force. It would be difficult to calculate the exact form of the potential energy, but we know that 5 = 0 gives the minimum energy, so the derivative vanishes there (f/ (0) = 0). We can do a Taylor expansion about the S = 0 potential energy minimum as we did in 

Chapter 3. This predicts that for a small enough distortion, the potential energy function looks essentially like that of a harmonic oscillator  

Thus the electron cloud will oscillate back and forth, just like a mass on a spring, or a child on a swing. 

As discussed in Section 6.3, a superposition of two states gives a probability distribution which oscillates at frequency o = ( )/ — El)/ft, and this is the same frequency 

FIGURE 8.2 Both Is and 2p orbitals give symmetric probability distributions. Combining the two into a superposition state breaks this symmetry, because the 2p orbital constructively interferes with Is in one lobe and destructively interferes in the other. 

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