3. Let X and P be the position and linear momentum operators of a single particle, respectively. The corresponding representations in one-dimensional position space are X = xb(x) dy(x) Puy = -ih dx where x is position and is a wavefunction. a) Find the commutator X, Consider the case of a particle of mass m in a 1-D box of length L, where the wavefunctions are sin(knx), 0 0 L' b) Show that n is an eigenfunction of the kinetic energy operator corresponding eigenvalue? What is the 2m c) Find < X >.

3. Let X and P be the position and linear momentum operators of a single particle, respectively. The corresponding representations in one-dimensional position space are X = xb(x) dy(x) Puy = -ih dx where x is position and is a wavefunction. a) Find the commutator X, Consider the case of a particle of mass m in a 1-D box of length L, where the wavefunctions are sin(knx), 0 0 L' b) Show that n is an eigenfunction of the kinetic energy operator corresponding eigenvalue? What is the 2m c) Find < X >.