Combined system state as product of states


by Sekonda
Tags: combined, product, state, states
Sekonda
Sekonda is offline
#1
Dec3-12, 12:14 PM
P: 209
Hey,

I have to express the combined system state of j=5/2, m=5/2 in terms of the products of states j1,m1 and j2,m2.

[tex]\mid j,m> =\mid\frac{5}{2},\frac{5}{2}>\: ,\: |j_1,m_1> \& |j_2,m_2>[/tex]

I know that one way of achieving this is for j1=3/2 and j2=1 but I'm not sure how to express this - I think this is involving Clebsch-Gordon coefficients.

Thanks guys,
SK
Phys.Org News Partner Physics news on Phys.org
Physicists design quantum switches which can be activated by single photons
'Dressed' laser aimed at clouds may be key to inducing rain, lightning
Higher-order nonlinear optical processes observed using the SACLA X-ray free-electron laser
DocZaius
DocZaius is offline
#2
Dec3-12, 12:28 PM
P: 287
Just from inspecting your J and M, it seems clear a (spin 3/2 with max m=3/2) and a (spin 1/2 with max m=1/2) would combine to that state. As a rule, if your M happens to be the sum of two particular spins' max m, then you have a straightforward product of the states at their max m.
Sekonda
Sekonda is offline
#3
Dec3-12, 12:34 PM
P: 209
I suppose I'm confused in how I could write that the 5/2, 5/2 state was the same as 3/2, 3/2 and a 1,1.

Would this simply be: [tex]|\frac{5}{2},\frac{5}{2}>=|\frac{3}{2},\frac{3}{2}>|1,1>[/tex]

I'm not really sure what is meant by the product of two states - what notation would be used.

Sekonda
Sekonda is offline
#4
Dec3-12, 12:35 PM
P: 209

Combined system state as product of states


or

[tex]|\frac{5}{2},\frac{5}{2}>=|\frac{3}{2},\frac{3}{2},1,1>[/tex]
DocZaius
DocZaius is offline
#5
Dec3-12, 01:09 PM
P: 287
I've always used the first one, myself. Not sure about the second.
Sekonda
Sekonda is offline
#6
Dec3-12, 01:11 PM
P: 209
Right cool, I thought so to but I'm just a bit confused with my notes - I have two very similar way of writing it. Cheers.
DocZaius
DocZaius is offline
#7
Dec3-12, 01:15 PM
P: 287
Also, I should add another condition to my rule above.

As a rule, if your M happens to be the sum of two particular spins' max m and J=M, then you have a straightforward product of the states at their max m. This holds true if you replace instances of "max" with min" in the previous sentence.
Sekonda
Sekonda is offline
#8
Dec3-12, 04:18 PM
P: 209
Indeed, this makes sense. Thanks for the help DocZaius!


Register to reply

Related Discussions
Product States Quantum Physics 8
H atom electron in combined spin/position state Advanced Physics Homework 3
Why can XRF and LIBS distinguish different valences and combined states of a element? General Physics 1
Finding State Matrix from given states in an autonomous Linear Dynamical System Linear & Abstract Algebra 0