Using the commutation relations between the Pauli matrices, show that: (a) e^i ασy σx e^-i ασy=σx cos(2 α) σz sin(2 α) (b) e^i ασz σx e^-i ασz=σx cos(2 α)-σy sin(2 α) (c) e^i ασx σy e^-i ασx=σy cos(2 α)-σz sin(2 α) | Numerade

b. (10 points) Explain what is the difference between the classical harmonic oscillator and the quantum harmonic oscillator in terms of their energy scheme (discrete or continuous). (Hint: you can draw the energy diagram of each oscillator and then you can use them for your explanation)? Explain the concept of quantization of energy using your own words? (Note: Your answer must be not less than five lines).

Lecture 9: Operator Methods for the Harmonic Oscillator | Quantum Physics I | Physics | MIT OpenCourseWare