01-28-2016, 04:08 AM
I was looking through old-ish threads and I saw you made a thread about doing a course on quantum mechanics but the thread was locked so I couldn't reply. But I was interested to see what stuff you covered / what approach was taken.
In the first year of my degree course, I did a bit of introductory QM, where we looked at the issues in physics that led to quantum theory - the ultraviolet catastrophe, the photoelectric effect and atomic spectra. Then we went through the developments leading up to the time-independent Schrodinger equation and solved it for simple situations. In second year, we did a course on QM which was basically the same thing, starting from the ultraviolet catastrophe and eventually arriving at the the time-dependent Schrodinger equation. Finding the uncertainty relation using the maths of wave packets (delta k . delta x has a minimum of 1, for a Gaussian wavepacket). Then we were just solving the Schrodinger equation in different situations - infinite potential wells, finite potential wells, potential barriers, hydrogen atom and quantum numbers. The Pauli exclusion principle. Then we did some statistical mechanics and showed that quantum effects gave a more realistic solution to the energy spectrum for a black body.
This year, I did a more mathematical QM course with state vectors and observables in a Hilbert space. We started with the postulates, then on to spin-half systems. Then, we just solved the Schrodinger equation for simple potentials, e.g. infinite potential wells, harmonic potentials. Then, we did angular momentum and demonstrated that spin in a form of intrinsic angular momentum. We finished with time-independent perturbation theory. Having done QM before, I found it interesting but, as a mathematical rather than physical course, there wasn't much actual physics involved - you could solve the problems without thinking of them as real physical situations. It was more about becoming fluent in the formalism rather than solving physical problems.
In the first year of my degree course, I did a bit of introductory QM, where we looked at the issues in physics that led to quantum theory - the ultraviolet catastrophe, the photoelectric effect and atomic spectra. Then we went through the developments leading up to the time-independent Schrodinger equation and solved it for simple situations. In second year, we did a course on QM which was basically the same thing, starting from the ultraviolet catastrophe and eventually arriving at the the time-dependent Schrodinger equation. Finding the uncertainty relation using the maths of wave packets (delta k . delta x has a minimum of 1, for a Gaussian wavepacket). Then we were just solving the Schrodinger equation in different situations - infinite potential wells, finite potential wells, potential barriers, hydrogen atom and quantum numbers. The Pauli exclusion principle. Then we did some statistical mechanics and showed that quantum effects gave a more realistic solution to the energy spectrum for a black body.
This year, I did a more mathematical QM course with state vectors and observables in a Hilbert space. We started with the postulates, then on to spin-half systems. Then, we just solved the Schrodinger equation for simple potentials, e.g. infinite potential wells, harmonic potentials. Then, we did angular momentum and demonstrated that spin in a form of intrinsic angular momentum. We finished with time-independent perturbation theory. Having done QM before, I found it interesting but, as a mathematical rather than physical course, there wasn't much actual physics involved - you could solve the problems without thinking of them as real physical situations. It was more about becoming fluent in the formalism rather than solving physical problems.
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