A particle is trapped in a 1-dimensional box along the y-axis between y=0 and y=5. The potential energy, V(y) of the box is zero for 0y5 and everywhere else. A wavefunction the form Y(y)=Acos(y+2)+Bsin(y+2), where A and B are constants, is suitable but needs to be refined. a. Assume that Y(y)=0 when y0. Apply the boundary conditions to this wavefunction to produce a better wavefunction. Be sure to show all work. b. Normalize your refined wavefunction from part a on the interval between y=0 and y=5. Be sure to show all your work. c. Calculate the energy for this particle - in - the - box. Assume it has the normalized wavefunction you calculated in part b. Be sure to show all your work. d. Extend your answer from part b to a 3-dimensional wavefunction suitable for a 3dimensional 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 0xa,0y5, and 0zc