Any help would be greatly appreciated. Even just a start. Any MATLAB help would be great or just how to go forward with the problem in general. Will thumbs up times a million :) ! Thanks!

The stationary Schrdinger equation for the harmonic oscillator reads E (x) 2m dr2 Discretize the position to transform this differential equation into a matrix eigenvalue equa- tion and write a MATLAB code to determine the energy spectrum. Turn in: a printout of the MATLAB code and a printout of the eigenvalues obtained. For ex- tra credit, plot the wavefunctions for the three states with the lowest energies. The following may help you to write the code: (10 points) e in terms of a rescaled variable y - Vfracmthx the Schrdinger equation reads i.e. apart from the overall energy scale fw you may set all constants equal to 1 and solve to do this, discretize position yna nd rplace the 2nd derivative by finite differences d2 . this yields a matrix eigenvalue equation with the kinetic energy matrix being band-diagonal 0-1 2 1 0 0 0 0 0 1 210 0 , 0 0 01 21 0 and the potential energy matrix being diagonal 0 4 0 0 0 0 0 Va2. 00 0 0 0 0 0 2 e look only at the lowest eigenvalues and make sure your results are converged both in the lattice spacing a as well as in the size of the matrix AN a good start is a 0.1 and N101... The stationary Schrdinger equation for the harmonic oscillator reads E (x) 2m dr2 Discretize the position to transform this differential equation into a matrix eigenvalue equa- tion and write a MATLAB code to determine the energy spectrum. Turn in: a printout of the MATLAB code and a printout of the eigenvalues obtained. For ex- tra credit, plot the wavefunctions for the three states with the lowest energies. The following may help you to write the code: (10 points) e in terms of a rescaled variable y - Vfracmthx the Schrdinger equation reads i.e. apart from the overall energy scale fw you may set all constants equal to 1 and solve to do this, discretize position yna nd rplace the 2nd derivative by finite differences d2 . this yields a matrix eigenvalue equation with the kinetic energy matrix being band-diagonal 0-1 2 1 0 0 0 0 0 1 210 0 , 0 0 01 21 0 and the potential energy matrix being diagonal 0 4 0 0 0 0 0 Va2. 00 0 0 0 0 0 2 e look only at the lowest eigenvalues and make sure your results are converged both in the lattice spacing a as well as in the size of the matrix AN a good start is a 0.1 and N101