Can't get Quantum Harmonic Oscillator Wave Function by ode45

Sho

2014 12 10

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I have just tested if I can get correct Quantum Harmonic Oscillator Wave Function by ode45 But the result doesn't looks like what it should be. What's problem? (I haven't used ode45 for a while, maybe some basic silly mistakes)

function Wavefcn
[x,Phi] = ode45(@WaveFunction,[0 10],[1 0]);
plot(x,Phi(:,1));
function dPhi = WaveFunction(x,phi)
n = 0; %grand state
eps = 2*n+1;
dPhi = zeros(2,1);
dPhi(1) = phi(2);
dPhi(2) = (x^2-eps)*phi(1);
end
end

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Sho 2014-12-10

Now I found it but I have to zoom it. Actually I want to do a more complicated job. In that case I probably don't know what the scale Phi would be(I have to normalise Phi later). Do you have some idea to avoid problem like it?

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