Quantum Mechanics I

Time evolution equation for quantum systems and the Hamiltonian operator. Wave functions, probability amplitudes, and expectation values for observables. Schrodinger equation and solutions for one-dimensional systems. Quantization. Postulates of quantum mechanics in the language of linear algebra. Observables, commutation relations, and conserved quantities. Generalized uncertainty principle. Time-energy uncertainty principle. Position and momentum operators and eigenstates. Separation of variables and solutions for three-dimensional systems; degenerate eigenvalues; application to Hydrogen atom. Spherically symmetric potentials. Angular momentum operators and eigenstates. Spin angular momentum. Spin-1/2 particle in a magnetic field. Addition of angular momentum and Clebsch-Gordon coefficients.