great explanation. So too many interactions to keep up with. Each particle has its own many interactions. There are many particles. So when u say the many body problem should involve an equation for each electron that takes into account all interactions.
For example, say we have 3 particles: A, B, C.
we would write one equation of motion for A. This equation taks into account the interaction A,B and A,C.
Another equation for particle B: here we see the interaction terms B,A and B,C.
Same for particle C: interaction terms A,C and C,B....
The 3 equations form a system of equation, right?
Now, we want to turn this single 3-body problem into 3 one-body problem....What would that mean?