(a) write down explicitly the properly normalized real-space wave function ψ(r, θ, φ; t) as state (4) evolves in time t.
(b) what is the expectation value e = ⟨hb⟩ of particle energy in this state. does this expectation value depend on time?
(c) find pressure p that the particle in this state exerts on the inner wall of the potential shell.

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?