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how to normalize results from ode45

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Simo
Simo on 10 May 2020
Answered: darova on 11 May 2020
I solved using the shooting method the first 3 level of the anharmonic quantum potential well
I get a plot like this
since I've found the three energys with fzero I simply run this code
Any suugest in how to normalize?
thank you
x=linspace(-0.5,+0.5);
V=alpha*x.^2+beta*x.^4;
xspan = [-0.5,0.5];
options = odeset('RelTol',1e-8,'absTol',[1e-8,1e-8]);
for i=1:length(ENERGIE)
Etrial=ENERGIE(i);
[T,Y] = ode45(@Anharmonic,xspan,init_cond,options);
plot(T,Y(:,1))
end

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darova
darova on 10 May 2020
What normalazing means?
Simo
Simo on 10 May 2020
Integrations of square modulus between -inf and +inf equal to 1

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Accepted Answer

darova
darova on 11 May 2020
What if just to scale the data?
clc,clear
x = -1:.1:1;
y = 2 - x.^2;
plot(x,y) % plot original data
s = trapz(x,y) % find area ander the curve
y1 = y/s; % scale data
line(x,y1) % plot scaled data
trapz(x,y1) % calculate area under the scaled curve

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