1. A particle is trapped in a 1-dimensional box along the y axis between y=0 and y=2. The potential energy, V(y) of the box is zero for 0 y 2 and everywhere else. A wavefunction the form (y) = ( +5pi/2) - Bsin(y-5pi/2) where A and B are constants, is suitable but needs to be refined. a) Assume that (y) = 0 when y < 0 and y > 2. Apply the boundary conditions to this wavefunction to produce a better wavefunction. Be sure to show all your work. b) Normalize your refined wavefunction from part a on the interval between y = 0 and y = 2. Be sure to show all your work. c) Calculate the energy for this particle-in-the-box. Assume is has the normalized wavefunction you calculated in part b. Be sure to show all your work. d) What is the particles momentum along the x-axis (no calculation is required)? Be sure to explain your reasoning. e) Extend your answer from part b to a 3-dimensional wavefunction suitable for a 3- dimensional particle in a box by making a well-reasoned guess. Assume the wavefunction exists at the box boundaries and within the box boundaries, but nowhere else. Beyond the box boundaries, the potential energy is . The box encloses the region bounded by 0 x a, 0 y 3, and 0 z c.