(Baby QM) Analytic Solution to the Infinite Square Well Problem

[obstinatus]

Hi,

I think I'm having a bit of a brain fart...I'm messing with this numerical code trying to understand the 1-D time-independent Schrödinger's equation infinite square well problem (V(x) infinite at the boundaries, 0 everywhere else). If normalized Phi squared is the probability of finding the particle in that location, what the heck is the analytical solution I should plot against it to see how close it is? The normalized wavefunction given by Hyperphysics is much too large. Any and all suggestions appreciated.

 

[nrqed]

Hi,

I think I'm having a bit of a brain fart...I'm messing with this numerical code trying to understand the 1-D time-independent Schrödinger's equation infinite square well problem (V(x) infinite at the boundaries, 0 everywhere else). If normalized Phi squared is the probability of finding the particle in that location, what the heck is the analytical solution I should plot against it to see how close it is? The normalized wavefunction given by Hyperphysics is much too large. Any and all suggestions appreciated.
View attachment 260814

What do you mean their wavefunction is too large? What specific wavefunction were you looking at?

 

[hilbert2]

That probability density function looks like it has to be multiplied with a constant greater than 50 to become normalized. Then you can compare it to the exact solution.

You can also find the correct multiplier by making a nonlinear curve fit to this data with function

$P (x) = C\sin^2 (2\pi x)$

and setting $C$ as the fitting parameter. This can be done in Origin Pro or some free program like Grace.