# Perturbation and Variational Theory

1. Dec 4, 2004

### Rachael_Victoria

Ok so I am trying to expand my understanding of these two concepts. Here is what I understand so far.
There are very few Schrodinger Equations that are exactly solvable
Both Theories are used to approximate a solution
Perturbation Theory utilizes a similar function with a known solution and adds the small perturbation to bring the answer closer to the actual value of the solution for the unsolvable wave function.
Variational Theory takes a trial wave function and sets up a set of parameters, a1, a2, etc and results in a value Ev. Ev is always larger than E, the actual ground state energy. Adjusting the parameters to minimize Ev will bring you closer and closer to the actual value of the ground state energy, for your actual wave function, E.
Is this correct and can any one expand on what I have here? I understand how to do the actual mathematics involved but am a little shaky on why I am doing them. Also if anyone has a clear definition of how the variational principal relates to Huckle theory I would really appreciate it.
Thanks

2. Dec 4, 2004

### dextercioby

Well,apparently u got the "big picture" right.And if u say that "details" (mathematical difficulties) are not a problem to u,then u got yourself a "touch down".U say u don't understand the point in making all those painful calculations??I believe your post has the answer inside.Exact methods in quantum theory are usable only in the case of isolated systems for which the Hamiltonian has a particular form,involving simple kinetical pieces (usually squares of momenta) and that the potential has a simple form which allows exact integrations.When all these don' t occur,i.e.the Hamiltonian has a sh**** part that spoils the beauty behind it all,then,in order to obtain by theoretical methods experimentally verifiable results,u need to make use of aproximate methods.Whether they're perturbative or not,it's less relevant.Mathematics will be the key.

Are u sure it's Huckle??I haven't read too much QM,but the only guy with a name close to his is Hueckel (with an umlaut,actually) and he formulated the molecular orbital method (MOM) to describe chemical bonds in molecules.If it isn't him,then i'm sorry i cannot be of any assistance anymore.

Good luck!!
Daniel.