Correspondence principle and its use

[janko78]

Can you give me some examples, link of correspondence principle use in life. All I have found out are theoretical examples such as Bohr's model...

If I understand right, correspondence principle says that simple equations used for classical examples with a few data and quantum equations used for larger data, give us pretty much the same results. If we'd use simple equations instead of quantum we'd make some mistake, but not to critical.

Is my thinking correct? Can you give me an example for its use in industry?

 

[DrClaude]

Your statement of the correspondence principle in incorrect. It says that as a quantum number increases, the behavior of the quantum system resembles more and more the classically equivalent system.

One example is the harmonic oscillator. While the ground state of the quantum HO has a a maximum probability in the middle of the potential, as you go higher in energy states, the probability starts to have maxima at the classical turning points of the potential.

I don't know of any practical use of this in industry. It is mostly useful to understand the quantum to classical transition.

 

[haushofer]

The modern notion of the principle doesn't apply only to qm, but also to classical physics. The Newtonian limit of general relativity is an example, or the c --> oo limit of special relativity giving Galilean relativity.

In physics we work with effective field thories. Some theories are more complete than others, and should contain 'older' theories. E.g. General Relativity should 'contain' Newtonian gravity, special relativity and Galilean relativity. I.e. it should imply these theories in certain limits. The correspondence principle tells you how the less complete theories are obtained by limiting procedures (involving the appropriate constants like h,c or G) of the more complete theories.

For QM you can take the h --> 0 limit in the path integral and use a saddle point approximation, which leaves you only with the path implied by the action principle. As such the correspondence principle can explain the role of the action in classical mechanics and the emergence of determinism.

Hope this helps :)

 

[janko78]

Thanks guys.

I've been looking for some literature about cor. principle in my hometown libraries but haven't found much (I found most about Bohr's cp). The thing is I need as much literature I can get, because it's my diploma research. A few pages won't be enough. I attend mechanical engineering faculty so literature should be about cor. principle in physics. I've been looking over the internet, but haven't found enough (Wikipedia and so it's not enough).

Can you give me some internet base of that kind of literature?