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4. Another way of visualizing 3D wave functions is to plot a slice along a particular plane. In Example 4.1, wave functions Ynim are found for the infinite spherical well potential. (See Eq. 4.51). Since the o dependence is fairly simple, we can see what is going on even if we restrict 0, and let e 0 2nt. In Cartesian coordinates, that is, we can look at y(x,0,z). Make plots of Unim(x, 0, z)|in the infinite spherical well potential with radius a = 1 for the values of nlm = (100), (200), (300),(110), (120). Hint: If you do this in Mathematica, there are handy functions that give you spherical harmonics and spherical Bessel functions. You will need to find the zeros of the spherical Bessel functions. Mathematica also has a handy function that gives you the zeros of (regular) Bessel functions, which can be related to zeros of spherical Bessel functions. Figure 4.2: Graphs of the first four spherical Bessel functions. Ynem (r, 9,) = Ant je (bne) Y" (0,0), , (4.51) ith the constant Ane to be determined by normalization. As before, the wave function is N 1 radial nodes 12 4. Another way of visualizing 3D wave functions is to plot a slice along a particular plane. In Example 4.1, wave functions Ynim are found for the infinite spherical well potential. (See Eq. 4.51). Since the o dependence is fairly simple, we can see what is going on even if we restrict 0, and let e 0 2nt. In Cartesian coordinates, that is, we can look at y(x,0,z). Make plots of Unim(x, 0, z)|in the infinite spherical well potential with radius a = 1 for the values of nlm = (100), (200), (300),(110), (120). Hint: If you do this in Mathematica, there are handy functions that give you spherical harmonics and spherical Bessel functions. You will need to find the zeros of the spherical Bessel functions. Mathematica also has a handy function that gives you the zeros of (regular) Bessel functions, which can be related to zeros of spherical Bessel functions. Figure 4.2: Graphs of the first four spherical Bessel functions. Ynem (r, 9,) = Ant je (bne) Y" (0,0), , (4.51) ith the constant Ane to be determined by normalization. As before, the wave function is N 1 radial nodes 12

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