Harmonic oscillator (25 marks): consider a linear harmonic oscillator with the solution de- fined by the ladder operators a and a defined in class. use the number basis in) to do the following. class. use the nuim such that (ψ x1) is as large as a) construct a linear combination of 10) and 11) to form a state l possible. b) suppose that the oscillator is in the state constructed in a) at time t = 0, write an expression to de- scribe the time dependence of this state state for t > 0. evaluate the expectation value (t) x r(t)) as a function of time for t > 0. c) defining (δ2p = (t)lx? it((t)x1r(t))2. calculate (ar)2

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day

mass and volume are the answers you are looking for