Questions and Answers
What does the polar diagram in Figure 7-7 represent?
The directional dependence of the eigenfunctions
For values of r which are small compared to $a_0/Z$, what can be said about the exponential term in the eigenfunctions?
The exponential term is slowly varying
How does the probability density depend on the coordinate $\phi$ for small values of r?
The probability density does not depend on $\phi$
What is the expression for the three-dimensional behavior of the eigenfunctions $\psi_{n,l,m}$?
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What is the relationship between the polar diagram in Figure 7-7 and the three-dimensional surface of the eigenfunctions?
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For small values of r, what can be said about the behavior of the electron near the nucleus?
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What is the form of the factor $\Theta_{l,m}(\theta)\Phi_{l,m}(\phi)$ presented in the text?
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How does the three-dimensional surface obtained by rotating the polar diagram represent the eigenfunctions?
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What is the relationship between the radial factor $R_{n,l}(r)$ and the directional factor $\Theta_{l,m}(\theta)\Phi_{l,m}(\phi)$ in the expression for the eigenfunctions?
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