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Subject offerings of new and developing areas of knowledge in mechanical engineering intended to augment the existing curriculum. See Class Schedule or departmental course information for topics and prerequisites. Course Information: May be repeated in the same or separate terms if topics vary.

Overview of quantum mechanics and the many-body Hamiltonian. Free electron gas, hydrogen atom, construction of basis sets, spherical harmonics. Simple molecules, large molecules, and the need for symmetry. Groups, group theory for crystallography, point groups, Bravais lattices. Induced representations, the rotation Lie group, Euler angles, quaternions, spherical tensors. Wigner/Clebsch-Gordon and Racah coefficients. Double groups, the symmetric/permutation group. Vibrations. Group theoretical approaches to machine learning: G-modules and Fourier transforms.