flag1 = 1; fs = 14; % fontsize time_step = 200; % jump frames Save animation flag2 % Save animation as a gif file (0 no) (1 yes) for flag2 flag2 = 1; % file name for animated gif ag_name = 'ag_se_fdtd_14.gif'; % Delay in seconds before displaying the next image = 0.0; % Frame to start frame1 = 0; The Schrodinger Equation and the FDTD Method The Schrodinger Equation is the basis of quantum mechanics. The state of a particle is described by its wavefunction which is a function of position and time The wavefunction is a complex variable and one can’t t. attribute any distinct physical meaning to it. We will consider solving the [1D] time dependent Schrodinger Equation using the Finite Difference Time Development Method (FDTD). The one time dependent Schrodinger equation for a particle of mass is given by m (1) where is the potential energy function for the system. The wavefunction is best expressed in terms of its real and imaginary parts is (2) Inserting equation 2 into equation 1 and separating real and imaginary parts results in the following pair of coupled equations
flag1 = 1; fs = 14; % fontsize time_step = 200; % jump frames Save animation flag2 % Save animation as a gif file (0 no) (1 yes) for flag2 flag2 = 1; % file name for animated gif ag_name = 'ag_se_fdtd_14.gif'; % Delay in seconds before displaying the next image = 0.0; % Frame to start frame1 = 0; The Schrodinger Equation and the FDTD Method The Schrodinger Equation is the basis of quantum mechanics. The state of a particle is described by its wavefunction which is a function of position and time t. The wavefunction is a complex variable and one can’t attribute any distinct physical meaning to it. We will consider solving the [1D] time dependent Schrodinger Equation using the Finite Difference Time Development Method (FDTD). The one time dependent Schrodinger equation for a particle of mass m is given by (1) where is the potential energy function for the system. The wavefunction is best expressed in terms of its real and imaginary parts is (2) Inserting equation 2 into equation 1 and separating real and imaginary parts results in the following pair of coupled equations
se_fdtd.docx