Originally Posted by

**Amiram** Hello, as I was studying quantum dynamics I ran into this simple looking differential equation for the spin of a particle:

dX/dt=w_{^}X , where w is the axis around which the spin processes (all in **R**^{3} of course). X is in fact also a function of space but let us assume that X(t,{q_{i}})= T(t)*Q({q_{i}}) where i=1,2,3 for any 3D coordinate system. From the cross product's distributive property we can deduce to a problem which X is a function of time only At first I tried solve the equations with pure algebra but the system had too many free variables. what I did managed to do is to find a private solution for w=(1,1,1) which is T(t)=e^-t(-2t-3,1,2+2t).

I'd be glad if someone could help with the general case, thank you.