Title: Quantum Xmas Ornaments
Post by: fractower on January 01, 2013, 01:55:27 AM
The wave functions for the electron states of Hydrogen can be found by finding the eigenstates of Schrödinger's equation
 = \frac{-\hbar^2}{2m}\nabla^2 \Psi(\mathbf{r}) + V(\mathbf{r}) \Psi(\mathbf{r})<br />)
Fortunately solutions can be found in a number of text books and on Wikipedia. Most sources only list the first 4 or so excited states since these are the ones that are physically relevant. However the eigenstates form a compete set like Fourier components so that any 3D complex scaler field can be reconstructed as a sum of the eigenstates.
Calling the eigenstates fractal is a bit of a stretch. The detail does not extend to the infinitesimally small like brots, bulbs and boxes but does extend to the infinitely large with larger quantum numbers.
I have attached some pictures of iso-surfaces of the real part of the higher eigenstates in festive holiday colours.
Fortunately solutions can be found in a number of text books and on Wikipedia. Most sources only list the first 4 or so excited states since these are the ones that are physically relevant. However the eigenstates form a compete set like Fourier components so that any 3D complex scaler field can be reconstructed as a sum of the eigenstates.
Calling the eigenstates fractal is a bit of a stretch. The detail does not extend to the infinitesimally small like brots, bulbs and boxes but does extend to the infinitely large with larger quantum numbers.
I have attached some pictures of iso-surfaces of the real part of the higher eigenstates in festive holiday colours.