(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A system in a state with L=1, S=1, J=2, Mj=2 and odd parity decay in a particle [tex]\Delta^-[/tex] (even parity and spin 1/2) and in a proton (even parity).

1) Find the possible momenta of S and L of the final system

2) Find the most general final system

3) Find the angular distribution of probability to find both particles with spin parallel to z axis.

3. The attempt at a solution

1)

Final S=0,1

Final L=2 (S=0) or L=1,2,3(S=1)

but L=1 and L=3 is not admissible due to the parity conservation

So there is only: S=0, L=2

or S=1, L=2

2)The two final states are

[tex]|2022>=|2020>[/tex]

[tex]|2122>=\frac{\sqrt{2}|2120>-|2111>}{\sqrt{3}}[/tex]

where the notation is: [tex]|L,S,J,Mj>=|L,S,m_L, m_S>[/tex]

I don't know in which of this two states the particle will decay, so I have to consider the general state:

[tex]\alpha|2020>+\beta\frac{\sqrt{2}|2120>-|2111>}{\sqrt{3}}[/tex]

with [tex]|\alpha|^2+|\beta|^2=1[/tex]

3) The probability is the [tex]|\frac{\beta}{3}Y_2^2|^2[/tex]

But I don't know how to find alpha and beta

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Quantum mechanics question

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**