Quantum Physics I

Instruction is in the form of lectures and calculation exercises. The course covers the following:<br> \- The emergence and structure of quantum theory: the interpretation and properties of the wave function, the superposition principle, wave packets, Heisenberg's uncertainty relation, the time-dependent Schrödinger equation, free particles, probability current and probability conservation, expectation values, the correspondence principle, operators, commutators, Hermitean operators, the time-independent Schrödinger equation, and stationary states.<br> \- Applications in one dimension: rectangular potentials, the harmonic oscillator, and the tunneling phenomenon.- The postulates and formalism of quantum mechanics: Dirac's bra-ket notation, Hermite conjugation, eigenfunctions as orthonormal bases, wave function collapse, compatible observables, the time evolution of expectation values, the general uncertainty principle. <br> \- Angular momentum: eigenfunctions for angular momentum operators, the Legendre polynomials and spherical harmonics, the rotation energy of molecules, general angular momentum and spin, spin in matrix bases, and addition of angular momenta, step operators.<br> \- Solution of the Schrödinger equation in three dimensions: separation ansätze, threedimensional rectangular and harmonic potentials, central potential, and the hydrogen atom.