The Spherical Harmonic functions Yl,m are the wavefunctions for any particle that is free to move in the spherical polar angles theta and phi (i.e., that has no dependence on these angles in the particle's potential energy function, as in the hydrogen atom). These graphs plot the real and imaginary parts of the spherical harmonics given in Table 12.2 on page 423. They are the building blocks for atomic wavefunctions in general, and their shapes and orientations in space are important to learn. Don't worry about their specific mathematical forms. Instead, concentrate on size, shape, and direction as the quanum numbers l and m change. You can change the values for l and m as you wish, but don't make l bigger than about 6 in order to keep the expression for Y on the page!
Since these are in general complex number functions with real
and imaginary parts, it takes two graphs to show them fully, one
for each part. The real part of the function is on the left, and
the imaginary part (if there is one!) is on the right. The x,
y, and z Cartesian axes are in black, and the
theta, phi spherical polar angular axes are in red.
Here's a question for you to answer. Do the functions change when
m is replaced by -m for any given l value? Can you give a physical
reason for your answer?
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