(a) for the case of two qubits, briefly explain the main difference between product states and entangled states. provide one example of each. (b) show that the identity between spin angular momentum operators s+s- = s2- s2 ± hs, holds. data: s s tisy, [se, sy] = ihs2, [sy, s2] = ihs, [s2, s = ihsy. (c) an s = 1/2 particle at t =0 is prepared in the following state x with respect to the eigen-spinors of s2: x= a 2 (e)r= where a is a normalisation constant. imagine many copies of the state x are prepared and measured. describe the possible outcomes of measurements of s2 and their probabilities (d) show that for a normalised trial state, vtrial), the ground state energy, eg. s., of a hamiltonian, h, is bounded as (trial|h\btrial). hence, prove that the first order perturbation theory estimate of the eg. s. ground state energy never under-estimates the true ground state energy.

Samir watches a 100-minute movie on his spaceship. maria's spaceshipe flies in the same direction as samir's spaceship but she observes his move to last 125 minutes and his spaceship to be 40 m long. how long does samir observe his own spaceship to be? according to an observer on earth, planet x is stationary. maria and samir depart earth on their spaceships at the same time, each flying at 0.5c. maria flies toward planet x and samir flies in the opposite direction. according to maria, her voyage to planet x takes 9 years. how many years does marias voyage take according to samir?

What changes occur in the brain during the teenage years? 25 points, someone me out!a.) thinking becomes slower as the brain grows larger. b.) connections between neurons become stronger and faster. c.) unused neurons fuse together to form larger, better functioning neurons. d.) more neurons are developed.

Astudent throws a water balloon with speed v0 from a height h = 1.76 m at an angle θ = 21° above the horizontal toward a target on the ground. the target is located a horizontal distance d = 9.5 m from the student’s feet. assume that the balloon moves without air resistance. use a cartesian coordinate system with the origin at the balloon's initial position. (a) what is the position vector, rtarge t, that originates from the balloon's original position and terminates at the target? put this in terms of h and d, and represent it as a vector using i and j. (b) in terms of the variables in the problem, determine the time, t, after the launch it takes the balloon to reach the target. your answer should not include h. (c) create an expression for the balloon's vertical position as a function of time, y(t), in terms of t, vo, g, and θ. (d) determine the magnitude of the balloon's initial velocity, v0, in meters per second, by eliminating t from the previous two expressions.