Here's a small preview of some topics you can expect to see:
- The Quantum Harmonic Oscillator Ladder Operators
- Newton's Laws
- The Dot and Cross Products
- And more...
Now, at this point, many texts define, with no motivation other than future ``convenience'', two operatorsSee you all there!
(5a)(5b)and proceed to show how these can be used to simplify the Hamiltonian and easily solve the problem. While it is an elegant and quick solution, this presentation is completely useless. I find it highly unlikely that Dirac sat down to solve this problem and tried a whole series of random operators
and so on, along with their complex conjugates, until he lucked out with the solution in (5)...from Behind the Guesses