MATLAB: How to solve a non homogeneous diff equation numerically

differential equationsquantum

I'm trying to solve a quantum harmonic oscillator numerically and I followed Matlab steps to crack the equation, however, it doesn't work. Any other idea for another method or where the mistake could be? the equation is d2psi/dx2=(constant-x^2)*psi Thanks for advanced
syms y(x)
k=23; m=9.1093821545*1e-31; w=sqrt(k/m);hb=(6.6260695729*1e-34)/(2*pi);E0=hb*w*.5;
[V] = odeToVectorField(diff(y, 2) == (hb*w*.5-.5*k*x.^2).*y);
x1=-sqrt(hb*w/k);
x2=-x1;
M = matlabFunction(V,'vars',{x,'Y'});
[m,n] = ode45(M,[x1 x2],[0. 0.]);

Best Answer

k=23; 
m=9.1093821545*1e-31; 
w=sqrt(k/m);
hb=(6.6260695729*1e-34)/(2*pi);
E0=hb*w*.5;
M=@(x,y)[y(2);(hb*w*.5-.5*k*x^2)*y(1)];
x1=-sqrt(hb*w/k);
x2=-x1;
[m,n] = ode45(M,[x1 x2],[0.; 0.]);
Result will be that y(1) and y(2) are identically zero.
Best wishes
Torsten.
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