Consider a physical system whose hamiltonian h and an operator a are given by 5 0 0 0 0 2 0 2 0 -2 0 0 1 0 a ao h e 0 1 where eo has the dimensions of energy (a) do h and a commute? if yes, give a basis of eigenvectors (b) which among the sets of operators h), {a}, {h, a), {i2, â) form a complete set of commuting operators (csco)? mon to h and a. com q18 show that the momentum and the total energy can be measured simultaneously only when the potential is constant everywhere.

Suppose you were asked to find the torque about point p due to the normal force n in terms of given quantities. which method of finding the torque would be the easiest to use?

Ablock of mass m = 2.5 kg is attached to a spring with spring constant k = 790 n/m. it is initially at rest on an inclined plane that is at an angle of 28 degrees with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is k = 0.14. in the initial position, where the spring is compressed by a distance of a = 0.18 m, the mass is at its lowest position and the spring is compressed the maximum amount. take the initial gravitational energy of the block as zero. b) if the spring pushes the block up the incline, what distance, l, in meters will the block travel before coming to rest? the spring remains attached to both the block and the fixed wall throughout its motion.

Suppose you have three polarizing filters, with the second at an angle of 42∘ to the first and the third at an angle of 90∘ to the first. by what perfect will the original intensity of unpolarized light be reduced to after passing through all three filters?