MATLAB: Unable to plot a wavefunction

functionplotting

Hi, I wonder if any of you can try to plot this and see if they also get a weird bar?

syms h g x C t m e p c 
h = 1.0545718E-34
g = 5.344285879E-28
E = 1
Z = - (exp(-(x*(g*1i + (- 2*g^2 + E)^(1/2)))/h)*(g*1i - (- 2*g^2 + E)^(1/2)))/(2*(E - 2*g^2)^(1/2)) + (exp(-(x*(g*1i - (- 2*g^2 + E)^(1/2)))/h)*(g*1i + (- 2*g^2 + E)^(1/2)))/(2*(E - 2*g^2)^(1/2))
fplot(real(Z),   [ -4, 4 ])
figure(1)

Thanks!

If so, why?

Best Answer

Hi Sergio,

This function appears to have scaling issues. If you plot

figure(1)
fplot(real(Z),   [-2*h, 2*h])
figure(21)
fplot(imag(Z),   [-2*h, 2*h])

you can see the function. I believe this addresses the question, but there are other things going on too. Possibly you were using E=1 just for test purposes, but compared to that value, 2*g^2 is infinitesimal. Also the function itself is an increasing exponential which is not good for a wave function unless there is some kind of hard boundary.

Related Solutions

MATLAB: How to use parameters in the upper and lower limits of an intergral

The same code works me without any error, including vpa(W). To decide number of digits, use the following:

vpa(W,3)

MATLAB: I need a final equation… second….

I'm not sure what is meant by "a to ha function are 'Random variable', so I will just phrase the answer as if they are arbitrary constants.

The first key to this is to tell solve() that x and z are to be solved for by adding parameters 'x','z' to the end of the calling sequence.

The solution from solve() might be expressed in terms of some RootOf() of a quadratic equations. I do not recall at the moment how to ask MuPad to expand those equations; in Maple the call to use is allvalues().

Then simplify() -- or in the case of Maple, simplify(%,size), which asks it do look for factorizations and so on.

The output is as follows, again two solutions.

{

x = (1/4263200)*(((1460*h-1460*f)*a+1460*b*(f-g))*(-9685390482496000000*(b^2-(1/2131600)*c^2+(1/1065800)*e*c-(1/2131600)*e^2-(1/2131600)*(f-h)^2)*(a^2-2*a*b+b^2-(1/2131600)*d^2+(1/1065800)*d*e-(1/2131600)*e^2-(1/2131600)*(g-h)^2)*((c-e)*a-(-d+c)*b)^2*(a^2-(1/2131600)*c^2+(1/1065800)*c*d-(1/2131600)*d^2-(1/2131600)*(f-g)^2))^(1/2)-4543718560000*(-(1/2131600)*((1/1460)*g+a-b-(1/1460)*h)*(-(1/1460)*g+a-b+(1/1460)*h)*c^3+((1/2131600)*e*a^2-(1/2131600)*b*(d+e)*a+(1/2131600)*b^2*d-(1/4543718560000)*(g-h)*((-e+d)*f+e*g-d*h))*c^2+(a^3*b+(-2*b^2-(1/2131600)*f^2+((1/2131600)*g+(1/2131600)*h)*f-(1/2131600)*g*h+(1/2131600)*e^2)*a^2+(b^2+(1/1065800)*f^2+(-(1/1065800)*g-(1/1065800)*h)*f+(1/532900)*g*h-(1/2131600)*h^2-(1/2131600)*d^2-(1/2131600)*e^2-(1/2131600)*g^2)*b*a+(-(1/2131600)*f^2+((1/2131600)*g+(1/2131600)*h)*f+(1/2131600)*d^2-(1/2131600)*g*h)*b^2-(1/4543718560000)*(g-h)*((h-g)*f^2+(g^2-h^2+d^2-e^2)*f-d^2*h+(e^2-h*(g-h))*g))*c-a^3*b*e+((d+e)*b^2-(1/2131600)*d*f^2+((1/1065800)*d*h-(1/2131600)*e*(g-h))*f-(1/2131600)*d*h^2-(1/2131600)*(e^2-h*(g-h))*e)*a^2-(b^2*d+(-(1/2131600)*d-(1/2131600)*e)*f^2+((1/1065800)*d*h+(1/1065800)*e*g)*f-(1/2131600)*d^2*e+(-(1/2131600)*h^2-(1/2131600)*e^2)*d-(1/2131600)*e*g^2)*b*a+(-(1/2131600)*e*f^2+(((1/2131600)*g-(1/2131600)*h)*d+(1/1065800)*e*g)*f-(1/2131600)*d^3-(1/2131600)*g*(g-h)*d-(1/2131600)*e*g^2)*b^2+(1/4543718560000)*((h-g)*f^2+(g^2-h^2+d^2-e^2)*f-d^2*h+(e^2-h*(g-h))*g)*((-e+d)*f+e*g-d*h))*((a-b)*c-a*e+d*b))/(((a-b)*c-a*e+d*b)*(((1/1460)*g+a-b-(1/1460)*h)*(-(1/1460)*g+a-b+(1/1460)*h)*c^2+(-2*e*a^2+2*b*(d+e)*a-2*b^2*d+(1/1065800)*(g-h)*((-e+d)*f+e*g-d*h))*c+(h^2+e^2+f^2-2*f*h)*a^2-2*b*(f^2+(-g-h)*f+d*e+g*h)*a+(f^2+d^2-2*f*g+g^2)*b^2-(1/2131600)*((-e+d)*f+e*g-d*h)^2))

z = (1460*(-9685390482496000000*(b^2-(1/2131600)*c^2+(1/1065800)*e*c-(1/2131600)*e^2-(1/2131600)*(f-h)^2)*(a^2-2*a*b+b^2-(1/2131600)*d^2+(1/1065800)*d*e-(1/2131600)*e^2-(1/2131600)*(g-h)^2)*((c-e)*a-(-d+c)*b)^2*(a^2-(1/2131600)*c^2+(1/1065800)*c*d-(1/2131600)*d^2-(1/2131600)*(f-g)^2))^(1/2)+((g-h)*d+(h-g)*e)*c^3+((2131600*b^2-4263200*a*b-e^2+2131600*a^2-d^2+2*d*e)*f+(-g+2*h)*d^2+(-g-h)*e*d+(2*g-h)*e^2-g^3+h*g^2+(-2131600*a*b+2131600*a^2+h^2)*g-h^3+(2131600*b^2-2131600*a*b)*h)*c^2+(((g-h)*d+(h-g)*e)*f^2+(d^3-d^2*e+(4263200*a*b-e^2-2131600*a^2-2131600*b^2+g^2-h^2)*d+e^3+(4263200*a*b-2131600*a^2+h^2-g^2-2131600*b^2)*e)*f-h*d^3+(2*g-h)*e*d^2+((-g+2*h)*e^2-h*g^2+(-h^2-2131600*b^2)*g+2*h^3+(-4263200*b^2+4263200*a*b+2131600*a^2)*h)*d-e^3*g+(2*g^3-h*g^2+(4263200*a*b+2131600*b^2-h^2-4263200*a^2)*g-2131600*h*a^2)*e)*c+(2131600*b^2-4263200*a*b-e^2+2131600*a^2-d^2+2*d*e)*f^3+(d^2*h+(-g-h)*e*d+e^2*g+(2131600*a*b-2131600*b^2)*g+(2131600*a*b-2131600*a^2)*h)*f^2+(-e*d^3+(2*e^2+2131600*a*b+h^2)*d^2+(-e^3+(-8526400*a*b+2131600*b^2-g^2-h^2+2131600*a^2)*e)*d+(g^2+2131600*a*b)*e^2+(2131600*a*b-2131600*b^2)*g^2+(2131600*a*b-2131600*a^2)*h^2+9087437120000*b^2*a^2-4543718560000*b^3*a-4543718560000*a^3*b)*f+e*h*d^3+((-g-h)*e^2+2131600*b^2*g-h^3+(2131600*b^2-2131600*a*b)*h)*d^2+(e^3*g+(h*g^2+(h^2-2131600*b^2)*g-2131600*h*a^2)*e)*d+(-g^3+(-2131600*a*b+2131600*a^2)*g+2131600*h*a^2)*e^2+2131600*b^2*g^3-2131600*b*g^2*a*h+(-2131600*b*a*h^2+4543718560000*b^3*a-4543718560000*b^2*a^2)*g+2131600*a^2*h^3+(4543718560000*a^3*b-4543718560000*b^2*a^2)*h)/(4263200*((1/1460)*g+a-b-(1/1460)*h)*(-(1/1460)*g+a-b+(1/1460)*h)*c^2+(4*(g-h)*(-e+d)*f+(-4*g*h+4*h^2+8526400*b*(a-b))*d-8526400*e*(-(1/2131600)*g^2+(1/2131600)*g*h+a*(a-b)))*c+4263200*((1/1460)*d+a-b-(1/1460)*e)*(-(1/1460)*d+a-b+(1/1460)*e)*f^2+(4*d^2*h-4*(g+h)*e*d+4*e^2*g-8526400*(a-b)*(a*h-g*b))*f+(4263200*b^2-2*h^2)*d^2+(-8526400*a*b+4*g*h)*e*d+(4263200*a^2-2*g^2)*e^2+4263200*(a*h-g*b)^2)

}

and

{

x = (1/4263200)*(((-1460*h+1460*f)*a-1460*b*(f-g))*(-9685390482496000000*(b^2-(1/2131600)*c^2+(1/1065800)*e*c-(1/2131600)*e^2-(1/2131600)*(f-h)^2)*(a^2-2*a*b+b^2-(1/2131600)*d^2+(1/1065800)*d*e-(1/2131600)*e^2-(1/2131600)*(g-h)^2)*((c-e)*a-(-d+c)*b)^2*(a^2-(1/2131600)*c^2+(1/1065800)*c*d-(1/2131600)*d^2-(1/2131600)*(f-g)^2))^(1/2)-4543718560000*(-(1/2131600)*((1/1460)*g+a-b-(1/1460)*h)*(-(1/1460)*g+a-b+(1/1460)*h)*c^3+((1/2131600)*e*a^2-(1/2131600)*b*(d+e)*a+(1/2131600)*b^2*d-(1/4543718560000)*(g-h)*((-e+d)*f+e*g-d*h))*c^2+(a^3*b+(-2*b^2-(1/2131600)*f^2+((1/2131600)*g+(1/2131600)*h)*f-(1/2131600)*g*h+(1/2131600)*e^2)*a^2+(b^2+(1/1065800)*f^2+(-(1/1065800)*g-(1/1065800)*h)*f+(1/532900)*g*h-(1/2131600)*h^2-(1/2131600)*d^2-(1/2131600)*e^2-(1/2131600)*g^2)*b*a+(-(1/2131600)*f^2+((1/2131600)*g+(1/2131600)*h)*f+(1/2131600)*d^2-(1/2131600)*g*h)*b^2-(1/4543718560000)*(g-h)*((h-g)*f^2+(g^2-h^2+d^2-e^2)*f-d^2*h+(e^2-h*(g-h))*g))*c-a^3*b*e+((d+e)*b^2-(1/2131600)*d*f^2+((1/1065800)*d*h-(1/2131600)*e*(g-h))*f-(1/2131600)*d*h^2-(1/2131600)*(e^2-h*(g-h))*e)*a^2-(b^2*d+(-(1/2131600)*d-(1/2131600)*e)*f^2+((1/1065800)*d*h+(1/1065800)*e*g)*f-(1/2131600)*d^2*e+(-(1/2131600)*h^2-(1/2131600)*e^2)*d-(1/2131600)*e*g^2)*b*a+(-(1/2131600)*e*f^2+(((1/2131600)*g-(1/2131600)*h)*d+(1/1065800)*e*g)*f-(1/2131600)*d^3-(1/2131600)*g*(g-h)*d-(1/2131600)*e*g^2)*b^2+(1/4543718560000)*((h-g)*f^2+(g^2-h^2+d^2-e^2)*f-d^2*h+(e^2-h*(g-h))*g)*((-e+d)*f+e*g-d*h))*((a-b)*c-a*e+d*b))/(((a-b)*c-a*e+d*b)*(((1/1460)*g+a-b-(1/1460)*h)*(-(1/1460)*g+a-b+(1/1460)*h)*c^2+(-2*e*a^2+2*b*(d+e)*a-2*b^2*d+(1/1065800)*(g-h)*((-e+d)*f+e*g-d*h))*c+(h^2+e^2+f^2-2*f*h)*a^2-2*b*(f^2+(-g-h)*f+d*e+g*h)*a+(f^2+d^2-2*f*g+g^2)*b^2-(1/2131600)*((-e+d)*f+e*g-d*h)^2))

z = (-1460*(-9685390482496000000*(b^2-(1/2131600)*c^2+(1/1065800)*e*c-(1/2131600)*e^2-(1/2131600)*(f-h)^2)*(a^2-2*a*b+b^2-(1/2131600)*d^2+(1/1065800)*d*e-(1/2131600)*e^2-(1/2131600)*(g-h)^2)*((c-e)*a-(-d+c)*b)^2*(a^2-(1/2131600)*c^2+(1/1065800)*c*d-(1/2131600)*d^2-(1/2131600)*(f-g)^2))^(1/2)+((g-h)*d+(h-g)*e)*c^3+((2131600*b^2-4263200*a*b-e^2+2131600*a^2-d^2+2*d*e)*f+(-g+2*h)*d^2+(-g-h)*e*d+(2*g-h)*e^2-g^3+h*g^2+(-2131600*a*b+2131600*a^2+h^2)*g-h^3+(2131600*b^2-2131600*a*b)*h)*c^2+(((g-h)*d+(h-g)*e)*f^2+(d^3-d^2*e+(4263200*a*b-e^2-2131600*a^2-2131600*b^2+g^2-h^2)*d+e^3+(4263200*a*b-2131600*a^2+h^2-g^2-2131600*b^2)*e)*f-h*d^3+(2*g-h)*e*d^2+((-g+2*h)*e^2-h*g^2+(-h^2-2131600*b^2)*g+2*h^3+(-4263200*b^2+4263200*a*b+2131600*a^2)*h)*d-e^3*g+(2*g^3-h*g^2+(4263200*a*b+2131600*b^2-h^2-4263200*a^2)*g-2131600*h*a^2)*e)*c+(2131600*b^2-4263200*a*b-e^2+2131600*a^2-d^2+2*d*e)*f^3+(d^2*h+(-g-h)*e*d+e^2*g+(2131600*a*b-2131600*b^2)*g+(2131600*a*b-2131600*a^2)*h)*f^2+(-e*d^3+(2*e^2+2131600*a*b+h^2)*d^2+(-e^3+(-8526400*a*b+2131600*b^2-g^2-h^2+2131600*a^2)*e)*d+(g^2+2131600*a*b)*e^2+(2131600*a*b-2131600*b^2)*g^2+(2131600*a*b-2131600*a^2)*h^2+9087437120000*b^2*a^2-4543718560000*b^3*a-4543718560000*a^3*b)*f+e*h*d^3+((-g-h)*e^2+2131600*b^2*g-h^3+(2131600*b^2-2131600*a*b)*h)*d^2+(e^3*g+(h*g^2+(h^2-2131600*b^2)*g-2131600*h*a^2)*e)*d+(-g^3+(-2131600*a*b+2131600*a^2)*g+2131600*h*a^2)*e^2+2131600*b^2*g^3-2131600*b*g^2*a*h+(-2131600*b*a*h^2+4543718560000*b^3*a-4543718560000*b^2*a^2)*g+2131600*a^2*h^3+(4543718560000*a^3*b-4543718560000*b^2*a^2)*h)/(4263200*((1/1460)*g+a-b-(1/1460)*h)*(-(1/1460)*g+a-b+(1/1460)*h)*c^2+(4*(g-h)*(-e+d)*f+(-4*g*h+4*h^2+8526400*b*(a-b))*d-8526400*e*(-(1/2131600)*g^2+(1/2131600)*g*h+a*(a-b)))*c+4263200*((1/1460)*d+a-b-(1/1460)*e)*(-(1/1460)*d+a-b+(1/1460)*e)*f^2+(4*d^2*h-4*(g+h)*e*d+4*e^2*g-8526400*(a-b)*(a*h-g*b))*f+(4263200*b^2-2*h^2)*d^2+(-8526400*a*b+4*g*h)*e*d+(4263200*a^2-2*g^2)*e^2+4263200*(a*h-g*b)^2)

}

Sorry, I know the formatting is not nice, but reformatting it by hand takes too much time.

Best Answer

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