You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: test_schrodinger.m
    path of file: ./repos/chebfun/tests/chebop2
    
    the code of the file until where you have to start completion: function pass = test_schrodinger( pref )
% Check constant coefficient schrodinger equation. 

if ( nargin < 1 ) 
    pref = chebfunpref(); 
end 
tol = 1000*pref.cheb2Prefs.chebfun2eps;

% w > V
V = 1;  %potential function 
w = 2;  % frequency
k = sqrt(w - V); % wave number by dispersion relation
d = [-10 10 0 1];
exact = chebfun2(@(x, t) exp(1i*(k*x-w*t)), d);
N = chebop2(@(u) 1i*diff(u,1,1) + diff(u,2,2) - V*u, d); 
N.lbc = exact(d(1),:); N.rbc = exact(d(2),:);
% N.dbc = chebfun(@(x) exp(-10*(x-.2).^2),d(1:2));   %wave packet.
N.dbc = exact(:,d(3));
u = N \ 0; 

pass(1) = ( norm(u - exact) < 10*tol ); 

% Superposition
% w > V
V = 1;  %potential function 
w = 2;  % frequency
k = sqrt(w - V); % wave number by dispersion relation
d = [-10 10 0 1];
exact = chebfun2(@(x, t) exp(1i*(k*x-w*t)) + exp(1i*(-k*x-w*t)), d);
N = chebop2(@(u) 1i*diff(u,1,1) + diff(u,2,2) - V*u, d); 
N.lbc = exact(d(1),:); N.rbc = exact(d(2),:);
% N.dbc = chebfun(@(x) exp(-10*(x-.2).^2),d(1:2));   %wave packet.
N.dbc = exact(:,d(3));
u = N \ 0; 

pass(2) = ( norm(u - exact) < 10*tol ); 


% w < V

V = 2;  %pot
    
function 
w = 2;  % frequency
k = sqrt(w - V); % wave number by dispersion relation
d = [-10 10 0 1];
exact = chebfun2(@(x, t) exp(1i*(k*x-w*t)), d);
N = chebop2(@(u) 1i*diff(u,1,1) + diff(u,2,2) - V*u, d); 
N.lbc = exact(d(1),:); N.rbc = exact(d(2),:);
% N.dbc = chebfun(@(x) exp(-10*(x-.2).^2),d(1:2));   %wave packet.
N.dbc = exact(:,d(3));
u = N \ 0; 

pass(1) = ( norm(u - exact) < 10*tol ); 

% Superposition
% w > V
V = 1;  %potential function 
w = 2;  % frequency
k = sqrt(w - V); % wave number by dispersion relation
d = [-10 10 0 1];
exact = chebfun2(@(x, t) exp(1i*(k*x-w*t)) + exp(1i*(-k*x-w*t)), d);
N = chebop2(@(u) 1i*diff(u,1,1) + diff(u,2,2) - V*u, d); 
N.lbc = exact(d(1),:); N.rbc = exact(d(2),:);
% N.dbc = chebfun(@(x) exp(-10*(x-.2).^2),d(1:2));   %wave packet.
N.dbc = exact(:,d(3));
u = N \ 0; 

pass(2) = ( norm(u - exact) < 10*tol ); 


% w < V

V = 2;  %potential function 
w = 1;  % frequency
k = sqrt(w - V); % wave number by dispersion relation
d = [-1 1 0 1];
exact = chebfun2(@(x, t) exp(1i*(k*x-w*t)), d);
N = chebop2(@(u) 1i*diff(u,1,1) + diff(u,2,2) - V*u, d); 
N.lbc = exact(d(1),:); N.rbc = exact(d(2),:);
% N.dbc = chebfun(@(x) exp(-10*(x-.2).^2),d(1:2));   %wave packet.
N.dbc = exact(:,d(3));
u = N \ 0; 

pass(3) = ( norm(u - exact) <tol );

end