Find the state with Sn = li of a spin-1 particle, where n =sin() i +cos() k, by rotating a state with Sz = li by angle () counterclockwise about the y axis using the rotation operator R(()j) = e-i'5'yEJ /h. Suggestion: Use the matrix representation (3.104) for Sy in the Sz basis and expand the rotation operator in a Taylor series. Work out the matrices through the one representing s; in order to see the pattern and show that 1 +cos() sin() 1- cos() 2 h 2 R(ej) + sin () sin () h cos() S2 basis h 1- cos() sin () 1 +cos() 2 h

Anonzero net force acts on a particle and does work. which one of the following statements is true? the kinetic energy of the particle changes, but the speed of the particle does not change. the kinetic energy of the particle does not change, but the speed of the particle does change. the kinetic energy of the particle changes, but the velocity of the particle does not change. the kinetic energy and the speed of the particle change, but the velocity of the particle does not change. the kinetic energy, speed, and velocity of the particle change.