Uncomfortable with Schrölinger's Equation.

[The Overlord]

Greetings again,

I am currently amusing myself by creating a simulation of an atom using C# and Unity 3D, however I find that I am not comfortable enough with Schrödinger's Equation to properly code it !
Do You have any good source material You could refer to Me?
Or better yet, are You good with these equations and can be found on Skype with ease?

Any help would be appreciated,
Thank You

-The Overlord

Edited September 27, 2014 by The Overlord

[timo]

It is not quite clear to me what a simulation of an atom is supposed to be. For the hydrogen atom, reasonably good analytical approximations exist that give you the energy eigenstates (Wikipedia should have then, if not they can be googled). More complicated atoms, particularly with multiple electrons are more complicated. To give an approximate order of complication: the hydrogen atom is taught to every physics or chemistry student in their 2nd year in 1-3 weeks as part of the QM introduction lecture. I took multi-electron systems as a half-year specialization course in theoretical physics in 3rd or 4th year.

 

So I will assume the standard hydrogen atom: What you could simulate is the time-development of a given initial state. The way to go forward with this is as follows: First, you find the basis of energy eigenstates. Then, you transform the original state in a superposition of these basis states. The time-evolution for the Schrödinger equation for these basis states is trivial, so expressed in this basis the time-evolution of your initial state becomes straightforward (more or less - it certainly helps having done it once). That is what you could simulate, and the probability density of the electron location is something you could visualize. That should already be quite a project.

 

There are a few details why I am not sure if it will actually work: You might have to take into account the "continuum states" in addition to the bound states. And I am not sure that something interesting will be seen (but if you are interested in the Schrödinger equation chances are you are interested in research, so maybe just try it). A related project I did in a "Computational Physics" course was a simulation of a harmonic oscillator. Same idea as with the hydrogen atom, but not plagued by potentially-relevant continuum states and guaranteed (by my experience of having done it) to have some visual effect: If you start with a wave packet around some location you will see it oscillate around.

 

If you are not tied to the atom and just want to play around with quantum mechanics, programming and visualization I suggest starting with the harmonic oscillator, even if it sounds less interesting. Once you leave the situation where a teacher gives you homework that is guaranteed to have a simple solution, even seemingly trivial tasks can turn out to be huge amount of work (e.g.: do not underestimate the effort to debug simulation code, especially if you are not very familiar with the system you simulate).

 

For particular reference material, I think it would help if you can be more specific about what you want to do - and maybe share your progress with us, later. I just read a book claiming that some personal consultants are paid a lot of money to tell people to break down their idea in 20-40 well-defined sub-steps