Use the raising and lowering operator method to compute (n |& 2n) and (n|p2|n) for the general harmonic oscillator energy eigenstate | n). use your result to verify that you reproduce the expected result for (n| h |n). data 2 н - 2m 1 242 = hw ( â*â + п 3 0, 1, 2, 3, en = hw 2 mw р 2fh mw mw 2h mw [a, a' 1

(a) assume the equation x = at^3 + bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. determine the dimensions of the constants a and b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.) (b) determine the dimensions of the derivative dx/dt = 3at^2 + b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.)