On Monday, June 23, 2014 9:18:29 PM UTC-4, Chris Maness wrote:
>
> I am trying to plot a superposition of two static states psi1 and psi2
> that compose a state system Psi. Here is my code so far:
>
>
I'm not sure what happened here. I should point out that you don't need
to declare a variable unless you are going to actually use it as a
math-style variable, as opposed to just using it as a name.
sage: var('n,a')
(n, a)
sage: hbar, m = 1,1
sage: psi(x,t,n)=sqrt(2/a)*sin(n*pi*x/a)*e^(-i*n^2*pi^2*hbar*t/(2*m*a^2));
sage: psi
(x, t, n) |--> sqrt(2)*sqrt(1/a)*e^(-1/2*I*pi^2*n^2*t/a^2)*sin(pi*n*x/a)
sage: Psi(x,t)=1/sqrt(2)*psi(x,t,1)+1/sqrt(2)*psi(x,t,2);
sage: Psi
(x, t) |--> sqrt(1/a)*e^(-2*I*pi^2*t/a^2)*sin(2*pi*x/a) +
sqrt(1/a)*e^(-1/2*I*pi^2*t/a^2)*sin(pi*x/a)
sage: P(x,t,a) = Psi.conjugate()*Psi
sage: P.expand()
(x, t, a) |--> sqrt(1/a)*conjugate(sqrt(1/a))*e^(-2*I*pi^2*t/a^2 +
2*I*pi^2*conjugate(t)/conjugate(a)^2)*sin(2*pi*x/a)*sin(2*pi*conjugate(x)/conjugate(a))
+ sqrt(1/a)*conjugate(sqrt(1/a))*e^(-1/2*I*pi^2*t/a^2 +
2*I*pi^2*conjugate(t)/conjugate(a)^2)*sin(pi*x/a)*sin(2*pi*conjugate(x)/conjugate(a))
+ sqrt(1/a)*conjugate(sqrt(1/a))*e^(-2*I*pi^2*t/a^2 +
1/2*I*pi^2*conjugate(t)/conjugate(a)^2)*sin(2*pi*x/a)*sin(pi*conjugate(x)/conjugate(a))
+ sqrt(1/a)*conjugate(sqrt(1/a))*e^(-1/2*I*pi^2*t/a^2 +
1/2*I*pi^2*conjugate(t)/conjugate(a)^2)*sin(pi*x/a)*sin(pi*conjugate(x)/conjugate(a))
sage: plot(P(x,1,1),x,0,1)
verbose 0 (2395: plot.py, generate_plot_points) WARNING: When plotting,
failed to evaluate function at 198 points.
verbose 0 (2395: plot.py, generate_plot_points) Last error message: 'unable
to simplify to float approximation'
but it plotted nicely - should it look like 1-abs(x-.5) ?
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