(20 marks total) Free particle in 1D (a) Obtain the wave function for a free quantum mechanical particle moving along the +ve x-axis with constant momentum p = k. (12 marks) (b) What is the Hamiltonian for the particle? Show that the state obtained in part (a) has constant energy. What is the energy? (8 marks) Hint: Set up the appropriate eigenvalue equation and solve for the eigenstate. You may use the orthogonality of the eigenfunctions to determine the integra- tion constant.