Tools of the Quantum Physicists

[bugatti79]

Folks,

I am reading some literature on QM. From what I understand QM can be used to great accuracy to predict the outcome of experiments and help to improve technology etc etc without having to worry to much about what it means i.e. the interpretations etc, i.e. the shut up and calculate approach.

I also read that QM can only provide analytical solutions to very simple cases like square wells, the simple oscillator which does not exist in reality.

So the question I have is what tools do Q physicists use in typical every work. Is it numerical methods/solutions mainly used instead of analytical methods to predict every quantum systems?

Cheers

 

[toombs]

Ah. You should read about the WKB approximation. And yes, a lot of the tools that quantum physicists and engineers use are numerical methods. Oh, you should also read about statistical mechanics. The theory of quantum physics is used regularly in statistical mechanics. So you could say quantum physics is only used directly with numerical methods, but it can be used indirectly with statistical mechanics, in particular with Fermi-Dirac statistics and Bose-Einstein statistics.

 

[A. Neumaier]

I also read that QM can only provide analytical solutions to very simple cases like square wells, the simple oscillator...

This is false.

There are a huge number of exactly solvable quantum systems, indeed, about as many as there are exactly solvable classical systems.

But even in classical mechanics, one doesn't get very far with exactly solvable models,
but has to use them in combination with perturbation theory.

For example, the problem of the motion of a classical system consisting only of the sun, the earth, and Jupiter cannot be solved exactly. nevertheless, we can predict the positions of all planets (an even more complex problem) very reliably.

Something similar holds for many quantum systems.