In gravity-free space, a 2.0-mg dust grain is confined to move back and forth between rigid walls 1.0 mm apart. (a) What is the speed of the dust grain if it is in the quantum ground state? (b) If it is actually moving at a speed of 0.25 mm/s, what is the quantum number associated with its quantum state?

In gravity-free space, a 2.0-mg dust grain is confined to move back and forth between rigid walls 1.0 mm apart. (a) What is the speed of the dust grain if it is in the quantum ground state? (b) If it is actually moving at a speed of 0.25 mm/s, what is the quantum number associated with its quantum state?