Obtaining expression for the angular momentum operator

How do you obtain an expression for L^2 (tbe angular momentum operator) in spherical polar from the expression for angular momentum L = R x P?

Do only part (d): Measuring Angular momentum A particle is in the state with wave function shi = 1/sqrt(2)[Y11 + Y1-1] (a) What value is obtained if L^2 is measured? (b) Does the particle have a definite value of Lz? (c) What are the probabilities of getting results h bar and - h bar and 0 for Lz? Are any other Lz results possible (d) Calculate (e) Suppose that when Lz is measured the result h bar obtained. What is the wave function afterwards?

Measuring Angular momentum A particle is in the state with wave function shi = 1/sqrt(2)[Y11 + Y1-1] (a) What value is obtained if L^2 is measured? (b) Does the particle have a definite value of Lz? (c) What are the probabilities of getting results h bar and - h bar and 0 for Lz? Are any other Lz results possible (d) Calculate (e) Suppose that when Lz is measured the result h bar obtained. What is the wave function afterwards?

Particle in a magnetic field

Could you please show me how to do the question attached? Don't do the parts that are crossed out in red. Thank you.

Equations of motion for expectation values

Could you please show me how to prove the relations in the MS Word problem attached? The problem is called Equations of motion for expectation values. Thank you.

Compatibility

Could you please show me how to do the problem that I have attached? I just want answers where momentum and energy commute and therefore have both definite values. Thank you.