matrix2.m

求解量子力学的薛定谔方程

%> The program <matrix2.m> solves for approximate eigenvalues 
%> using the matrix diagonalization methods built into MATLAB.
%> Hamiltonian = kinetic part + potential defined in [0,1],
%> Boundary conditions: u(0) = u(1) = 0. The potential is chosen 
%> from a set defined in <pot1.m> using <choice.m>, and the 
%> strength of it is defined by a multiplier. The multiplier must  
%> be chosen large enough in order to get interesting effects. 
%> Recall the scale of the spectrum of a particle confined to 
%> [0,1] is  E = (n*pi)^2/2, approx = 5, 20, 44, 79, 123, 178, ..
%> The basis set are harmonic functions in [0,1] adapted to the BCs.
%> The matrix elements of the kinetic energy are diagonal and exact, 
%> those of the potential are calculated using the FFT. Then the 
%> eigenvalues the resulting finite matrix are ound using the  
%> MATLAB <eig> algorithm and a few are displayed graphically.
%> 
%>
%>