Consider the following state of a harmonic oscillator at t = 0 written as a linear combi- nation of eigenstates of the number operator n|n) = nin), [ you may recall that the ladder operator a can be written 2h 2mhu (a) using the schrödinger equation, derive an expression for (t)) (b) calculate ()x(t) and ((t)x2(t) c) calculate < p > t-0 and show that it is a maximum when α . (d) calculate (0l(t) to derive an expression of the probability of being in the ground state as a function of time

Identical marbles are released from the same height on each of the following four frictionless ramps . compare the speed of the marbles at the end of each ramp. explain your reasoning

A2k pendulum has a speed of 1 m/s at a height of 1/2 meter

Afisherman notices that his boat is moving up and down periodically without any horizontal motion, owing to waves on the surface of the water. it takes a time of 2.20 s for the boat to travel from its highest point to its lowest, a total distance of 0.670 m . the fisherman sees that the wave crests are spaced a horizontal distance of 5.80 m apart. (a) how much is the wavelength? (b) find the period of the wave. (c) how fast are the waves traveling? (d) what is the amplitude a of each wave?