Classical mechanics: from Lagrangian to Hamiltonian, single particle formalism, small oscillations, normal modes, Hamilton-Jacobi theory, Hamilton's equation, review of wave mechanics: Schroedinger equation, barrier tunneling, quantum wells, mathematical foundation of quantum mechanics: ket space, representations, observables, eigenstates and diagonization, quantum postulates, application of quantum postulates to two-level systems, harmonic oscillators, creation and annihilation operators. Quantization of angular momentum, spherical harmonics, rotation operators, Landau levels, central force: hydrogen atom. Path integral formalism for quantum theory.
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