problem in defining functional with one input as function

I am trying to solve schrodinger equation using RK4 method my function is giving me error saying

Error using psi

K must be a scalar.

for t=1:Nt

psi_dasht=@(t,psi)(i.*((psi(X+dx,t)+psi(X-dx,t)-2.*psi(X,t))/2*dt^2 -V.*psi(X,t)));

k1=psi_dasht(X,psi(X,t));

k2=psi_dasht(X,psi(X,t)+0.5*dt.*k1);

k3=psi_dasht(X,psi(X,t)+0.5*dt.*k2);

k4=psi_dasht(X,psi(X,t)+dt.*k3);

psi(X,t+dt)=psi(X,t)+(dt/6).*(k1+2.*k2+2.*k3+k4);

end

function [a]=psi(x,t)

[a(t)]=(exp(-(x).^2/(2*4))/sqrt(2*pi*4));

end

[gotjen]

Please use code formating on your code.

Answer 1

[Vatsal]

Hi,

On running the provided code, I got the following error:

Declaring a variable with the same name as the local function "psi" is not supported in scripts.

The code uses "psi" as a function name and also as a variable to store values. You need to differentiate between the function "psi" and the variable that stores its values.

Here is a revised version of the provide code assuming "psi" is meant to be a matrix:

% Define the initial condition for psi
psi = zeros(length(X), Nt); % Preallocate psi for all X and t
psi(:,1) = initial_psi(X); 

for t = 1:Nt-1
    psi_dasht = @(X,psi) (i.*((psi([2:end, 1]) + psi([end, 1:end-1]) - 2.*psi)./dx^2 - V.*psi));
    k1 = psi_dasht(X, psi(:,t));
    k2 = psi_dasht(X, psi(:,t) + 0.5*dt.*k1);
    k3 = psi_dasht(X, psi(:,t) + 0.5*dt.*k2);
    k4 = psi_dasht(X, psi(:,t) + dt.*k3);
    psi(:,t+1) = psi(:,t) + (dt/6).*(k1 + 2.*k2 + 2.*k3 + k4);
end

% Define the initial_psi function
function psi_initial = initial_psi(X)
    psi_initial = exp(-X.^2 / (2*4)) / sqrt(2*pi*4);
end

I hope this helps!