Please find the mistake in this code.

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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)')
  6 Comments
Sam Chak
Sam Chak on 8 Jul 2022
Can you plot the lines manually one by one? You'll definitely find out what went wrong then.

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Accepted Answer

Torsten
Torsten on 8 Jul 2022
Edited: Torsten on 8 Jul 2022
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)')

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