Interaction between wave functions

[alpha_wolf]

Is there a version/subfield of QT that models the interactions between different wavefunctions? Something like Newtonian mechanics, but on the wavefunction level. E.g. you have two wave functions of (x,y,z,t), and you use the functions to find when and how they would affect each other and what would happen next and so on.

 

[ZapperZ]

Is there a version/subfield of QT that models the interactions between different wavefunctions? Something like Newtonian mechanics, but on the wavefunction level. E.g. you have two wave functions of (x,y,z,t), and you use the functions to find when and how they would affect each other and what would happen next and so on.

There is a reason why this question doesn't make sense. The wavefuction within QM is supposed to describe the ENTIRE system under consideration. Not partially, not only the one on the left, but the full system. It means that if there are two things that "interact" with one another, the appropriate wavefunction consists of BOTH things. One does not write the wave function of one, and then have that interact with the wavefunction of other. If you do that, then you haven't found the appropriate wavefunction to describe the system.

It is also this reason that in many practical cases, it is almost impossible to find the exact wavefunction. This is especially true in condensed matter physics, where we are dealing with a gazillion particles interacting with each other. One has to know how to write the wavefunction of ALL the gazillion particles. This is where many-body theory comes in and allows us to deduce the appropriate many-body "wavefunction" using Second Quantization formulation.

Zz.

 

[arivero]

This is where many-body theory comes in and allows us to deduce the appropriate many-body "wavefunction" using Second Quantization formulation.

Zz.

And then a series of rules to get the many-body wavefunctions from composition of separate single-body ones. Which , by the way, answers the question of the original poster.

 

[LURCH]

This sounds a lot like interferometry. Is it considered a form of interferometry, and is it at all similar to the type used in astronomy or laser detection?

 

[ZapperZ]

And then a series of rules to get the many-body wavefunctions from composition of separate single-body ones. Which , by the way, answers the question of the original poster.

Even that isn't appropriate all the time since more often than not, you do not even have a "wavefunction" to construct, much less know if the local combination of atomic orbitals is valid. The use of the "single-particle" Green's function is in fact a clear "resignation" to our inability to come up with such wavefunction. But even that has its limitation especially in the regime where there are no well-defined quasiparticles and the Green's function is meaningless.

Zz.