Many Body Problem Question

[foodchain]

In many body problems does the uncertainty principal lead to the difficulty of predicting quantum behavior for a molecular structure?

 

Another way I will word the question is that if the uncertainty principal is physically responsible for say the wavefuntion of a molecule? As such that the uncertainty principal itself in relation to superposition is what you are observing at any giving moment in say a many body system or molecule.

[timo]

I don't think uncertainty really add difficulty into obtaining the molecular structure as a WF except in the sense that you cannot pin down a single electron with two 3-tuples position and momentum but have to describe it with a whole R³->C function. I am not sure if I really would say that describing an object with a WF rather than two 3-tuples is a result of uncertainty. It's tied (at least for the uncertainty between momentum and position) but I personally feel that "it's due to uncertainty" gives uncertainty too much credit. In practice, QM calculations for more complicated objects use simplifications (the most straightforward being to treat the nuclei or the ions with the innermost shells classically) and/or some sophisticated methods like Density Functional Theory.

 

I think I have a relatively simple approximation that shows that even for a very simple molecule (H2, iirc) a straightforward solution is not achievable due to the huge amount of data (was something like "if you burn it to CDs you'd need all the mass of the visible universe to create enough CDs"). Sadly, the lecture notes that it's in -assuming I still have it at all, I threw away quite a lot of stuff lately- are in my other flat at which I won't be until next week. I'll post the example here next week if I happen to still have the notes and if I have access to the internet. It might show why and how the amount of data explodes. If someone else has a similar or the same example calculation (I imagine it being quite a standard example) please post it here - saves me time for searching

 

In short: I don't see uncertainty as problematic when it comes to finding a wave function. I'd rather see the fact that you describe an object via WFs (and not via R³ vectors) as tied to uncertainty.

[foodchain]

In short: I don't see uncertainty as problematic when it comes to finding a wave function. I'd rather see the fact that you describe an object via WFs (and not via R³ vectors) as tied to uncertainty.

 

Would it be a joke then to say you cant prove that past the uncertainty principal:D

 

No thanks for the reply though. Would that more or less be suggestive of the line of thinking that the wavefunction is more or less a possibly imperfect tool but that the uncertainty principal is a real physical property of quantum mechanical systems?