Find the following expectation values for and electron in the ground state of a harmonic oscillator potential. 7- a. and . b. and . [hint: no new integration allowed for this part.]

Asolid cylinder and a cylindrical shell have the same mass, same radius, and turn on frictionless, horizontal axles. the cylindrical shell has light-weight spokes connecting the shell to the axle. a rope is wrapped around each cylinder and tied to blocks of equal masses that are held the same height above the ground. both blocks are released simultaneously. the ropes do not slip. which block hits the ground first? or is it a tie?