Angular momentum conservation at quantum level how angular momentum of system is conserved when electron jumps higher energy state to lower energy state and photon is emitted(circularly polarized)? i read somewhere that it is NOT conserved .Why?
 A: The selection rules for atomic transitions are entirely governed by how much angular momentum the photon can carry away. A dipole transition (in the nomenclature, E1 or M1, depending on its parity) carries away angular momentum $\hbar$, so the atom's initial and final state must have angular momentum quantum numbers $J$ differing by zero or one.  A quadrupole transition (E2 or M2) carries away angular momentum $2\hbar$, so the atom's initial and final $J$ must differ by zero, one, or two.  Higher multipoles can carry more angular momentum, but are rarer. 

So if the photon carries away one unit of angular momentum, how can you have a transition where the atom's angular momentum $J$ is unchanged?  The answer comes from the way you add angular momentum vectors in quantum mechanics.  Suppose I have 
$$
\mathbf J = \mathbf J_1 + \mathbf J_2
$$
Thinking classically,


*

*if $\mathbf J_1$ and $\mathbf J_2$ are parallel, the magnitude of $\mathbf J$ should be $J = J_1 + J_2$; 

*if $\mathbf J_1$ and $\mathbf J_2$ are antiparallel, the magnitude of $\mathbf J$ should be $J = \left|J_1 - J_2\right|$; 


Those limits are respected. It's what happens in the middle that's a little wonky: if $\mathbf J_1$ and $\mathbf J_2$ make some angle with each other, shouldn't I be able to make $J$ have any value?  I can, but with the caveat that $J$ is still an integer (which is the "quantum" part of quantum mechanics).
So it's possible for an atom to emit a dipole photon, with spin $\hbar$, in a transition from a state with spin $J_\text{initial} = 3\hbar$ to a different state with spin $J_\text{final} = 3\hbar$. This is possible if $\mathbf J_\text{inital}$ and $\mathbf J_\text{final}$ point in different directions — in which case their projections $m_\text{inital},m_\text{final}$ onto your favorite quantization axis must also be different, and must be different by the photon's spin projection $m_\text{photon}$ onto that same axis.  
So far as we know, angular momentum is always conserved in a closed system.
