ur MATLAB (or other progr am) codes with line nme 1. Finite Difference Method (100 pts) - Requires Programming In class, we solved analytically the "particle in a box" (or "quantum well") problem to get the quantized energy levels of electrons in a confining potential. Remember that we first had to guess the solution of the differential equation (i.e., Schrdinger equation) with a certain general form (e.g., plane or sinusoidal waveforms with some unknown constants) which seemed to satisfy the Schrdinger equation. This approach is the simplest and somewhat effective, but if your initial guess happens to be not too good, then you are unlikely able to solve it. Now let's solve the same problem numerically at this time by means of finite-difference method that we learned in class 1-1. (20 pts) Construct a N by N Hamiltonian matrix by applying the following conditions, in a similar way that we did in class. For this problem (1-1), you are not required to run the simulation Just write down your answer. Show your work to get the full credit. - Select a one-dimensional discrete lattice with N points spaced by a Apply the boundary condition of Set U(x)-0 for 0