The hamiltonian of a spin in a magnetic field is given by a(bbysy+b, s), where α and the three components of b are all constants. (a) compute the energies and corresponding eigenstates of this system (b) let by-0 and b = 0. (i) use the energies and eigenstates for this case to determine the time evolution ψ(t) of a state with initial condition ψ(0) (ii) calculate the expectation values 〈s) and (s) as a function of tine. (iii) use a taylor expansion to show that the time-evolution operator u(t) exp(-iht/h) can be written as (e)s()i - isin(ut)x, where i is the identity operator, x (2/h)s, and w ab/2. hint: use the pauli matrix representation of the spin operator and show that

The ballistic pendulum was invented in 1742 by english mathematician benjamin robins. it consists of an initially stationary pendulum that moves after being struck by a bullet, and it is used to measure the original velocity of the bullet. the known variables are the bullet's mass m, the pendulum's mass m, and the height to which the block and bullet swing, determined by the length of the pendulum l and final angle θ. two principles of physics are necessary to solve for the bullet's original velocity. what are these principles? conservation of momentum and newton's third law conservation of energy and conservation of angular momentum grade summary deductions 0% potential 100% conservation of momentum and newton's second law. newton's second law and conservation of angular momentum. conservation of energy and newton's third law conservation of momentum and conservation of angular momentum. conservation of momentum and conservation of energy conservation of energy and newton's second law.

The softest and hardest minerals are: softest hardest

How would a small bar magnet be oriented when placed at position x?