Hi,

Seem to be a bit stuck. Here's my code:
 

Thanks in advance :-) 

Hi, 

I'm being unable to plot the solution to the equation

schro := {-(diff(psi(x), x, x))+(2*a*b*x^4+a^2*x^6+(b^2-a*(2*p+3))*x^2-(2*p+1)*b)*psi(x) = 0};

for the special cases of a=b=1 and p=0 and p=1

I've used dsolve and am getting Heun functions :-(

The claim is that the solutions come out to be exponentials of the form:

psi(x)=(x^p)*exp(-(a*(x^4))/4 - (b*(x^2))/2)

thanks in advance

Howdy!!

Just thought I'd put a quick one in. I'm trying to solve the Schrodinger equation given as:

under the constraint

I'm trying to plot this for a range of values of the parameters a,b and fixed p=0,1.

I'm aiming to get a solution of the form

and plotting it.

Thanks in advance

Hi,

Does anyone no how to normalize wavefunctions such that the plot on the right looks like the one on the left.

Here's my code:-

schro := {diff(psi(x), x, x)-(alpha*x^4+x^2-energy)*psi(x) = 0};

ic := {psi(3) = 0, (D(psi))(3) = 1};

Ic := [{psi(3) = 0, (D(psi))(3) = -1}, %$2];

E := [1.06538, 3.306, 5.74796];

schro1 := [seq(subs(energy = e, alpha = .1, schro), e = E)];

soln1 := [seq(dsolve(schro1[i] union Ic[i], {psi(x)}, type = numeric), i = 1 .. nops(E))]; with(plots);

display(seq(odeplot(soln1[i], [x, psi(x)], -3 .. 3, color = [red, blue, green][i]), i = 1 .. nops(E)))

Thanks in advance

Hi, I have been trying to solve the Schrodinger equation for harmonic oscillators using dsolve and plot the the wavefunctions for the different energy levels. However I am struggling to plot all the different wavefuntions on the same plot. I also want to normalize the wavefunctions to help compare their shapes and values. Here's my code:- schro := {diff(psi(x), x, x)-(alpha*x^4+x^2-energy)*psi(x) = 0}; // d / d \\ / 4 2 \ \ { |--- |--- psi(x)|| - \alpha x + x - energy/ psi(x) = 0 } \\ dx \ dx // / ic := {psi(3) = 0, (D(psi))(3) = 1}; {psi(3) = 0, D(psi)(3) = 1} schro1 := subs(energy = 3.30687, alpha = .1, schro); soln1 := dsolve(schro1 union ic, {psi(x)}, type = numeric); // d / d \\ / 4 2 \ \ { |--- |--- psi(x)|| - \0.1 x + x - 3.30687/ psi(x) = 0 } \\ dx \ dx // / proc(x_rkf45) ... end; with(plots); [animate, animate3d, animatecurve, arrow, changecoords, complexplot, complexplot3d, conformal, conformal3d, contourplot, contourplot3d, coordplot, coordplot3d, densityplot, display, dualaxisplot, fieldplot, fieldplot3d, gradplot, gradplot3d, implicitplot, implicitplot3d, inequal, interactive, interactiveparams, intersectplot, listcontplot, listcontplot3d, listdensityplot, listplot, listplot3d, loglogplot, logplot, matrixplot, multiple, odeplot, pareto, plotcompare, pointplot, pointplot3d, polarplot, polygonplot, polygonplot3d, polyhedra_supported, polyhedraplot, rootlocus, semilogplot, setcolors, setoptions, setoptions3d, shadebetween, spacecurve, sparsematrixplot, surfdata, textplot, textplot3d, tubeplot] odeplot(soln1, [x, psi(x)], -3 .. 3); Thank in advance