numbers The set of numbers are called the eigenvalues and set of vectors are the En. En eigenvectors. This is a single Matlab function that finds both the eigenvalues and eigenvectors. The syntax of the command is [e_funct, e_values] = eig(H) where is an (N-2)(N-2) matrix with the column corresponding to the nth nth e_funct eigenfunction and is a column vector for the eigenvalues in increasing order. N e_values Only the negative values of are significant. To obtain the complete eigenvector e_values we need to include the end points where . A sample Malab code [se_solve.m] to obtain the discrete set of eigenvalues and normalized eigenfunction is % All Eigenvalues 1, 2 , ... n where E_N < 0 flag = 0; n = 1; while flag == 0 E(n) = e_values(n,n); if E(n) > 0, flag = 1; end; % if n = n + 1; end % while E(n-1) = []; n = n-2; % Corresponding Eigenfunctions 1, 2, ... ,n: Normalizing the wavefunction for cn = 1 : n psi(:,cn) = [0; e_funct(:,cn); 0]; area = simpson1d((psi(:,cn) .* psi(:,cn))',xMin,xMax); psi(:,cn) = psi(:,cn)/sqrt(area); prob(:,cn) = psi(:,cn) .* psi(:,cn); end % for A potential well as shown in Figure (5) has a minimum at = 0 and tends to zero away x from the origin. A classical particle would be trapped by this potential well and oscillate to and fro about = 0 because the force on the particle is always directed towards origin x for position since = -dU/dx. F
numbers En. The set of numbers En are called the eigenvalues and set of vectors are the eigenvectors. This is a single Matlab function that finds both the eigenvalues and eigenvectors. The syntax of the command is [e_funct, e_values] = eig(H) where e_funct is an (N-2)(N-2) matrix with the nth column corresponding to the nth eigenfunction and e_values is a column vector for the N eigenvalues in increasing order. Only the negative values of e_values are significant. To obtain the complete eigenvector we need to include the end points where . A sample Malab code [se_solve.m] to obtain the discrete set of eigenvalues and normalized eigenfunction is % All Eigenvalues 1, 2 , ... n where E_N < 0 flag = 0; n = 1; while flag == 0 E(n) = e_values(n,n); if E(n) > 0, flag = 1; end; % if n = n + 1; end % while E(n-1) = []; n = n-2; % Corresponding Eigenfunctions 1, 2, ... ,n: Normalizing the wavefunction for cn = 1 : n psi(:,cn) = [0; e_funct(:,cn); 0]; area = simpson1d((psi(:,cn) .* psi(:,cn))',xMin,xMax); psi(:,cn) = psi(:,cn)/sqrt(area); prob(:,cn) = psi(:,cn) .* psi(:,cn); end % for A potential well as shown in Figure (5) has a minimum at x = 0 and tends to zero away from the origin. A classical particle would be trapped by this potential well and oscillate to and fro about x = 0 because the force on the particle is always directed towards origin for position since F = -dU/dx.
schrodinger.docx