In this assignment we will are attempting to find an approximate solution to the ground state energy of a particle constrained on the positive z-axis in the one- dimensional well (1) V(x) = We can use units h = m = 1 to simplify calculations. In these units the Hamiltonian is H -{-20 J-xe-/a, x>0 otherwise = 1 2 dr + V(x), x > 0. Question 1 Variational Method To start we will apply the variational theorem to obtain an approximate solution to the ground state energy (a) Sketch the potential, indicating the effect of a and X. Sketch the ground state wavefunction in the potential. (b) Use the variational method to estimate the ground state energy for X = 2 and a = 2. Consider any reasonable trial function you like, parameterised in as many variables a, 3,... as you like. Take (H) (26/26) and find the minimum energy with respect to your parameters (2) E = DE = ... = 0. 3 Your job is to get the lowest energy in the class. If you have difficulty, try using the trial function from the question below.