There is the philosophical approach to Quantum Mechanics which examines how and why everything works this way, and then there is the method my University professors pushed on us: "Shut up and Calculate!" Schrodinger Equation, Hilbert Spaces, just the straight math and how to use it to get real answers to quantum physics problems like particle in a box, or a 1D, 2D, or 3D infinite well. Or just getting the simplest atom Hydrogen right, and getting the spectral emissions and intensities.
: Sample physics and astrophysics from the MSci degree course - Gravitation and Cosmology (U. Virginia), ASTM003 AM and Accretion in Astrophysics (QMUL), STG problems cont., 1B24 Waves Optics and Acoustics exam (UCL), 2B24 Atomic and Molecular Physics, 2246 Mathematical Methods III (UCL), 2B29 EM Theory, 3C24 Nuclear and Particle Physics, 2B22 Quantum Physics problems 4, ASTM052 EGA-PoG (QMUL), ASTM116 Astrophysical Plasmas Ch. solns, ASTM001 Solar System, ASTM041 Rel Astro courseworks, 3C34 Physics and Evolution of Stars (UCL), 3C25 Solid State Physics, 1B45 (1B71) Mathematical Methods for Physics I.
Quantum Physics Problem Proved Unsolvable
See, in quantum physics problems with a loop group as the symmetrygroup, these symmetries tend to hold only up to a phase. The preciseway these phases work depends on the parameter q. Mathematically, thismeans that instead the loop group itself, the symmetries are reallydescribed by a slightly larger group that keeps track of these phases,called a "central extension" of the loop group. This has led people to spend huge amounts of energy studying representations of centralextensions of loop groups - which turn out to be much more economicallyunderstood, in a rather subtle way, as representations of quantum groups. In all this work the parameter q plays a major role.