http://www.physics.udel.edu/~jim/PHYS424_17F/Class%20Notes/Class_5.pdf by James MacDonald shows it well.
The operators are a natural guess on the lines of "if p and x were integers".
And then we can prove the ladder properties easily.
The commutator appear in the middle of this analysis.
- Quantum harmonic oscillator | 130, 235, 3
- Solutions of the Schrodinger equation | 34, 2k, 34
- Schrodinger equation | 555, 4k, 55
- Non-relativistic quantum mechanics | 26, 4k, 60
- Quantum mechanics | 170, 19k, 257
- Particle physics | 137, 29k, 482
- Physics | 276, 42k, 744
- Natural science | 0, 52k, 1k
- Science | 0, 57k, 1k
- Ciro Santilli's Homepage | 262, 197k, 3k