Quantum Harmonic Oscillator: Power series method in Maple

In the previous blog post What is Computational Physics (Science)?, I ended the post with the following figure

Graph of the probability distribution of the 100th state of the quantum
harmonic oscillator (generated using the power series method).

and stated that I might write a post on how to solve the Quantum harmonic oscillator numerically using the power series method (the other method being the ladder operator method [1]) and generate that figure. This post is just about that.

Ok. First I need to clear the cache with the restart command, import the PDEtools (to solve the pde SE) and Maplets[Elements] (necessary if you want to generate a maplet with a slider) packages.
with(PDEtools): #we need to use the dchange command later in the solution


Extraterrestrials & the Digital Universe -Von Neumann & Edward Teller


I've been reading George Dyson's Turing's Cathedral lately & today I read something interesting about intelligent life & computers from the age of John von Neumann & Edward Teller, which I'd like to share [1]:
Von Neumann rarely discussed extraterrestrial life or extraterrestrial intelligence; terrestrial life and intelligence were puzzling enough.

..."There is every reason to believe that any planet on which a large variety of molecules can reproduce by interconnected (or symbiotic) autocatalytic reactions, may see the formation of organisms with the same properties." One of these properties, independent of the local conditions, might be the development of the Universal Machine.
Over long distances, it is expensive to transport structures, and in expensive to transmit sequences. Turing machines, which by definition are structures that can be encoded as sequences, are already propagating themselves, locally, at the speed of light.


IPython: Python at your fingertips

To install the IPython notebook, do the following:

sudo apt-get install distribute ipython python-zmq python-tornado ipython-notebook
pip install numpy matplotlib #if you want to use the numpy extension & matplotlib plotting library
ipython notebook # launch the notebook from a terminal (will open in browser!)