Write down the time independent Schrödinger equation for the harmonic oscillator potential. Then confirm that the ground state wave function (n = 0) is a solution with the energy En = (1/2 + n)hw, n = 0,1,2,3... (plug in the function, differentiate, and confirm it is a solution).

An astronaut in space cannot use a scale or balance to weigh objects because there is no gravity. but she does have devices to measure distance and time accurately. she knows her own mass is 77.4 kg , but she is unsure of the mass of a large gas canister in the airless rocket. when this canister is approaching her at 3.50 m/s , she pushes against it, which slows it down to 1.30 m/s (but does not reverse it) and gives her a speed of 2.60 m/s . what is the mass of the canister?