- #1
James Jackson
- 162
- 0
I'm intregued as to what route people learned QM to whatever level you're at. I was taught the 'classic' way - classical mechanics, fields, mathematics, statistical physics etc first, before moving onto the derivation of the 1D Schrodinger equation for a free particle (without operators etc, the intuitive modifying of the classical wave equation to satisfy the de Broglie conditions). This, of course, leads to solutions of the wavefunction for infinite square wells, potential barriers etc. From there the 3D equation was discussed, followed by a first look at spherical harmonics in the solution for the hydrogen atom.
The next step was the move to an operator based approach, which is where the true beauty really begins to be seen - previously quoted results just 'dropping out' of the mathematics, something which, of course, becomes even more amazing when looking at QFT.
I feel that I would have preferred to be taught linear algebra first and start from an operator based approach, as this is the language of QM. Whilst starting with a purely calculus approach does indicate where things are going, I feel it hides the subtle beauty...
The next step was the move to an operator based approach, which is where the true beauty really begins to be seen - previously quoted results just 'dropping out' of the mathematics, something which, of course, becomes even more amazing when looking at QFT.
I feel that I would have preferred to be taught linear algebra first and start from an operator based approach, as this is the language of QM. Whilst starting with a purely calculus approach does indicate where things are going, I feel it hides the subtle beauty...