Assignment No. 1 (contd.) You will use Newton-Raphson method to find the eigenvalues. So we rewrite the equations as: fever (E) = VE + Vo sin (a VE+ Vo) V-E cos (a VE + Vo ) = o fodia( E) = VE + Vo...

Extracted text: Assignment No. 1 (contd.) You will use Newton-Raphson method to find the eigenvalues. So we rewrite the equations as: fever (E) = VE + Vo sin (a VE+ Vo) V-E cos (a VE + Vo ) = o fodia( E) = VE + Vo cos (a VE+ Vo) + v-E sin (a VE + Vo) = 0 COS To find the eigenvalues of the even states, you must find the zeros of fever (E) and for the odd states you must find the zeros of fodd(E). To use the Newton-Raphson method, you will also need to find the deriva- tives of these functions. Write a MATLAB code to implement the Newton-Raphson Method. Now comes the need for physical insight. Recall three conclusions from your Phy 301 course: (1) For symmetric systems, the lowest eigenstate is always an even state, and (2) The eigenstates alternate between even and odd states, and (3) the bound state eigenvalues lie between 0 and -Vo. So first find the lowest eigenvalue Eo by solving ferer(E) = 0 and your starting guess should be close to -Vo. To find the next eigenvalue Ej solve fodad(E) = 0 and your starting guess should be just a little bit above Eo. Then find E2 by solving fever (E) = 0 with starting guess slightly above E and so on.