Introduce the Algebra of Observables in classical mechanics and the transition to quantum mechanics through the principle of least action and Hamiltonian Mechanics .
A comprehensive lecture series should follow a logical progression from the mathematical foundations to more complex physical systems: Lectures on Quantum Mechanics for Mathematics S...
Focus on Hilbert Spaces , linear operators, and Spectral Theory . Use Dirac notation ( ) to represent states and measurements. Introduce the Algebra of Observables in classical mechanics