Please find the mistake in this code.

Reference image: plot should be like this but don't know where I am making mistake.

syms x lambda
warning off
alpha = -0.1;
sigma = 0.1;
eps = -0.1;
e = 0.2;
M = 10;
a = 2;

figure
psi_list = [10, 20, 30, 40. 50];
for i = 1:numel(psi_list)
    psi = psi_list(i);
    hbar = @(x) a - a.*x  + x;
    A1 = eps + alpha^3 + (3 * sigma^2 * alpha);
    B1 =@(x,lambda)  (-3 * lambda * M) * ((hbar(x).^2) + (2 .* hbar(x) .* alpha) + (sigma^2) + (alpha^2));

    a1 =@(x) tanh(M .* hbar(x));
    b1 =@(x) 1 - ((tanh(M .* hbar(x))).^2);
    c1 = (M * alpha) - ((M^3 * A1)/3);
    d1 = @(lambda) 2 * (M^2) * (1 + lambda);  
    
    C1=@(x)  a1(x) + (b1(x) .* c1);
    D1 =@(x,lambda)  d1(lambda) .* ((hbar(x).^3) + (3 .* (hbar(x).^2) .* alpha) + (3 .* hbar(x) .* (alpha)^2) + (3 .* hbar(x) .* (sigma)^2) + eps + (3 * alpha * (sigma^2)) + (alpha^3));

    f1 =@(x,lambda) B1(x,lambda) + (3 * lambda .* C1(x) .* hbar(x)) + (3 * lambda .* C1(x) .* alpha) + (D1(x,lambda) .* C1(x));
    f2 =@(x,lambda)  12 * (M^2) * (1 + lambda) .* C1(x);
    f3 = psi * (e^3);
    f4 = @(lambda) (1 + lambda) *180 * ((1 - e)^2);  
    f5 =@(lambda)  1/(2 + lambda);

    F = @(x,lambda) ((f5(lambda) .* f1(x,lambda))./f2(x,lambda)) + (f3/f4(lambda));

    q1 =@(x,lambda)  hbar(x) ./ (2 .* F(x,lambda));
    Q1 =  int(q1,x,0,1);    % integration with respect to "x" limit 0 to 1

    q2 = @(x,lambda) 1./(F(x,lambda));
    Q2 =  int(q2,x,0,1);    % integration with respect to "x" limit 0 to 1

    Q = @(lambda) Q1(lambda)/Q2(lambda); % Q is a function of "lambda"

    p1 = @(x,lambda) (1./F(x,lambda)) .* ((0.5 .* hbar(x)) - Q(lambda));
    P = @(x,lambda)  int(p1,x);    % integration with respect to "x" limit 0 to x
    % W is obtained by integrating "P" with respect to x limit to x is 0 to

    % 1
    W =@(lambda) int(P,x,0,1);

    fplot(@(lambda) W(lambda))

end

legend(num2str(psi_list'))
ylim([0 1])
xlim([0 4])
set(gca, 'ytick', 0:0.1:1);
set(gca, 'xtick', 0:0.2:4);
xlabel('lambda')
ylabel('W(lambda)')

[dpb]

No have symbolic TB here, sorry.

I'd suggest working through logic w/ debugger to see where it fails to do as expected first...

[Steven Lord]

warning off

I strongly recommend you not do this. MATLAB doesn't issue warnings "just because", it issues warnings because it sees something in the code that may cause a problem later or may indicate that the code isn't doing what you think it's doing.

So when you eliminate that line of code, what warnings get issued? Show the full and exact text of those messages (all the text displayed in orange in the Command Window.) Those warnings may very well explain why you're not seeing anything on your axes.

[AVINASH SAHU]

Warning: Error updating FunctionLine.

 The following error was reported evaluating the function in FunctionLine update: Invalid indexing or function definition. Indexing must follow MATLAB
 indexing. Function arguments must be symbolic variables, and function body must be sym expression.
 
Warning: Error updating FunctionLine.

 The following error was reported evaluating the function in FunctionLine update: Invalid indexing or function definition. Indexing must follow MATLAB
 indexing. Function arguments must be symbolic variables, and function body must be sym expression.
 
Warning: Error updating FunctionLine.

 The following error was reported evaluating the function in FunctionLine update: Invalid indexing or function definition. Indexing must follow MATLAB
 indexing. Function arguments must be symbolic variables, and function body must be sym expression.
 
Warning: Error updating FunctionLine.

 The following error was reported evaluating the function in FunctionLine update: Invalid indexing or function definition. Indexing must follow MATLAB
 indexing. Function arguments must be symbolic variables, and function body must be sym expression.
 
Warning: Error updating FunctionLine.

 The following error was reported evaluating the function in FunctionLine update: Invalid indexing or function definition. Indexing must follow MATLAB
 indexing. Function arguments must be symbolic variables, and function body must be sym expression.
 

sorry I forgot to apply "hold on" command. After applying this I am getting the above mentioned warning

[AVINASH SAHU]

syms x lambda
% warning off
alpha = -0.1;
sigma = 0.1;
eps = -0.1;
e = 0.2;
M = 10;
a = 2;

figure
hold on
psi_list = [10, 20, 30, 40. 50];
for i = 1:numel(psi_list)
    psi = psi_list(i);
    hbar = @(x) a - a.*x  + x;
    A1 = eps + alpha^3 + (3 * sigma^2 * alpha);
    B1 =@(x,lambda)  (-3 * lambda * M) * ((hbar(x).^2) + (2 .* hbar(x) .* alpha) + (sigma^2) + (alpha^2));

    a1 =@(x) tanh(M .* hbar(x));
    b1 =@(x) 1 - ((tanh(M .* hbar(x))).^2);
    c1 = (M * alpha) - ((M^3 * A1)/3);
    d1 = @(lambda) 2 * (M^2) * (1 + lambda);  
    
    C1=@(x)  a1(x) + (b1(x) .* c1);
    D1 =@(x,lambda)  d1(lambda) .* ((hbar(x).^3) + (3 .* (hbar(x).^2) .* alpha) + (3 .* hbar(x) .* (alpha)^2) + (3 .* hbar(x) .* (sigma)^2) + eps + (3 * alpha * (sigma^2)) + (alpha^3));

    f1 =@(x,lambda) B1(x,lambda) + (3 * lambda .* C1(x) .* hbar(x)) + (3 * lambda .* C1(x) .* alpha) + (D1(x,lambda) .* C1(x));
    f2 =@(x,lambda)  12 * (M^2) * (1 + lambda) .* C1(x);
    f3 = psi * (e^3);
    f4 = @(lambda) (1 + lambda) *180 * ((1 - e)^2);   
    f5 =@(lambda)  1/(2 + lambda);

    F = @(x,lambda) ((f5(lambda) .* f1(x,lambda))./f2(x,lambda)) + (f3/f4(lambda));

    q1 =@(x,lambda)  hbar(x) ./ (2 .* F(x,lambda));
    Q1 =  int(q1,x,0,1);    % integration with respect to "x" limit 0 to 1

    q2 = @(x,lambda) 1./(F(x,lambda));
    Q2 =  int(q2,x,0,1);    % integration with respect to "x" limit 0 to 1

    Q = @(lambda) Q1(lambda)/Q2(lambda); % Q is a function of "lambda"

    p1 = @(x,lambda) (1./F(x,lambda)) .* ((0.5 .* hbar(x)) - Q(lambda));
    P = @(x,lambda)  int(p1,x);    % integration with respect to "x" limit 0 to x
    % W is obtained by integrating "P" with respect to x limit of x is 0 to
    % 1
    W =@(lambda) int(P,x,0,1);
    
    fplot(@(lambda) W(lambda))

end

legend(num2str(psi_list'))
ylim([0 1])
xlim([0 4])
set(gca, 'ytick', 0:0.1:1);
set(gca, 'xtick', 0:0.2:4);
xlabel('lambda')
ylabel('W(lambda)')

Warning: Error updating FunctionLine.

The following error was reported evaluating the function in FunctionLine update: Invalid indexing or function definition. Indexing must follow MATLAB indexing. Function arguments must be symbolic variables, and function body must be sym expression.

[Sam Chak]

@AVINASH SAHU

Can you plot the lines manually one by one? You'll definitely find out what went wrong then.

[AVINASH SAHU]

okay thank you

Answer 1

[Torsten]

alpha = -0.1;
sigma = 0.1;
eps = -0.1;
e = 0.2;
M = 10;
a = 2;
%figure
psi_list = [10, 20, 30, 40, 50];
lambda = 0:0.2:4;
for i = 1:numel(psi_list)
    psi = psi_list(i);
    hbar = @(x) a - a.*x  + x;
    A1 = eps + alpha^3 + (3 * sigma^2 * alpha);
    B1 =@(x,lambda)  (-3 * lambda * M) * ((hbar(x).^2) + (2 .* hbar(x) .* alpha) + (sigma^2) + (alpha^2));
    a1 =@(x) tanh(M .* hbar(x));
    b1 =@(x) 1 - ((tanh(M .* hbar(x))).^2);
    c1 = (M * alpha) - ((M^3 * A1)/3);
    d1 = @(lambda) 2 * (M^2) * (1 + lambda);
    
    C1=@(x)  a1(x) + (b1(x) .* c1);
    D1 =@(x,lambda)  d1(lambda) .* ((hbar(x).^3) + (3 .* (hbar(x).^2) .* alpha) + (3 .* hbar(x) .* (alpha)^2) + (3 .* hbar(x) .* (sigma)^2) + eps + (3 * alpha * (sigma^2)) + (alpha^3));
    f1 =@(x,lambda) B1(x,lambda) + (3 * lambda .* C1(x) .* hbar(x)) + (3 * lambda .* C1(x) .* alpha) + (D1(x,lambda) .* C1(x));
    f2 =@(x,lambda)  12 * (M^2) * (1 + lambda) .* C1(x);
    f3 = psi * (e^3);
    f4 = @(lambda) (1 + lambda) *180 * ((1 - e)^2);
    f5 =@(lambda)  1./(2 + lambda);
    F = @(x,lambda) ((f5(lambda) .* f1(x,lambda))./f2(x,lambda)) + (f3./f4(lambda));
    q1 =@(x,lambda)  hbar(x) ./ (2 .* F(x,lambda));
    Q1 =  @(lambda)integral(@(x)q1(x,lambda),0,1,'ArrayValued',true);    % integration with respect to "x" limit 0 to 1
    q2 = @(x,lambda) 1./(F(x,lambda));
    Q2 =  @(lambda)integral(@(x)q2(x,lambda),0,1,'ArrayValued',true);    % integration with respect to "x" limit 0 to 1
    Q = @(lambda) Q1(lambda)./Q2(lambda); % Q is a function of "lambda"
    p1 = @(x,lambda) (1./F(x,lambda)) .* ((0.5 .* hbar(x)) - Q(lambda));
    P = @(x,lambda)  integral(@(y)p1(y,lambda),0,x,'ArrayValued',true);    % integration with respect to "x" limit 0 to x
    % W is obtained by integrating "P" with respect to x limit to x is 0 to
    % 1
    W =@(lambda) integral(@(x)P(x,lambda),0,1,'ArrayValued',true);
    
    %fplot(@(lambda) W(lambda))
    plot(lambda,W(lambda))
    hold on
end
legend(num2str(psi_list'))
ylim([0 1])
xlim([0 4])
set(gca, 'ytick', 0:0.1:1);
set(gca, 'xtick', 0:0.2:4);
xlabel('lambda')
ylabel('W(lambda)')

[AVINASH SAHU]

Thank you so much. It helped me a lot