Parts to include in a wavefunction

[benjammin]

Hi all,

I was wondering if anyone could help me with some general rules for which parts one should include in a wave function when trying to determine symmetry. In simple cases, we see things like $$\psi_{\rm space}\psi_{\rm spin},$$ and in more complicated cases we see $$\psi_{\rm space}\psi_{\rm spin}\psi_{\rm isospin},$$ and sometimes $$\psi_{\rm C-parity}$$ is included, etc. How can I tell when to include which pieces? I know it's related to the conservation laws for the particular reaction, but I've seen plenty of strong interaction states written without the $$\psi_{\rm C-parity},$$ even though C is conserved in those reactions. So I'm looking for some consistent rules.

Thanks!

 

[eljose79]

Determining the symmetry of a wave function can be a complex task, as it depends on the specific system and reaction being studied. However, there are some general rules that can help guide you in determining which parts to include in a wave function. These rules are based on the conservation laws for the particular reaction, as you mentioned.

First, it is important to consider the symmetries that are conserved in the reaction. This includes space (parity), spin, and isospin. If these symmetries are conserved, then the wave function should include terms that reflect these symmetries. For example, if spin is conserved, then the wave function should include a term for spin.

In some cases, additional symmetries may need to be considered, such as charge conjugation (C-parity). This symmetry is related to the conservation of charge and can be included in the wave function if it is conserved in the reaction.

However, there may be cases where a symmetry is conserved, but it is not necessary to include it in the wave function. This could be due to the specific properties of the system or the reaction. In these cases, it is important to carefully consider the symmetries and their conservation laws to determine which parts should be included in the wave function.

In summary, when determining the symmetry of a wave function, it is important to consider the conservation laws for the particular reaction and include terms that reflect these symmetries. However, it is also important to carefully consider the specific properties of the system and the reaction to determine which symmetries are necessary to include in the wave function. I hope this helps and best of luck in your studies!