How are particle simplices associated into complex particles?

Question

Nonfundamental particles are seen as made up of fundamental particles (in whatever specific theory).

consider the simple case of 2 simplex particles (subscript 1 and 2) which form a complex particle (no subscripts):

• Are $\phi(x_1), \phi(x_2)$ enough to determine $\phi(x_1,x_2)$ or is additional interaction information necessary?

• How is $\phi(x)$ related to $\phi(x_1,x_2)$? i.e. how is the wavefunction of the complex particle as a function of the complex particle position related to the wavefunction of the complex particle as a function of the individual subparticle positions? I would wildly guess to use barycentric centering: $\phi(x)=\int \phi(x_1,x_2)\delta(x - \frac{m_1 x_1+m_2 x_2}{m_1+m_2}) d x_1 d x_2$. But does that really make any sense and does it violate normalization of the resulting wavefunction etc?

now consider a collection of N simplex particles

• In classical physics one could use the energy of the particle to say if it is bound or not, how does this translate to conditions on the wavefunctions?
• One can envision 2 seperate solar systems in classical mechanics, where solar system 1 is not bound to solar system 2, but within each solar system the planets are bound to their star. Given only the positions and velocities of the stars and planets, is boundedness association possible in classical physics? how does one recognice that they form 2 stellar systems which are not bound, but withing stellar systems planets are bound?
• How does one do a similar association given wavefunctions of subparticles to identify which subparticles form a complex particle?

Or does none of the above make any sense?

Answer 1

Some of these questions are discussed in H. J. Lipkin's book "Quantum Theory: new approaches to selected topics". For example, the author considers an example of deuterons and shows how anti-commutation relations for the creation/annihilation operators for the constituent particles (neutrons and protons) lead to approximate commutation relations for the creation/annihilation operators for deuterons. The interaction information (describing the neutron-proton bound state) is extensively used. There is a lot of fascinating material there, so I cannot present it here.