Simulació d`experiments Stern- Gerlach consecutius

Simulació d’experiments SternGerlach consecutius
Lluís Garrido
[email protected]
http://www.ecm.ub.es/~garrido
Spin 1/2
1
La simulació....
+h/2
P1
| S z ,+ > →
−h/2
x gen
x=0
P1
Si
x =1
1 − P1
xgen < P1
+h/2
recordatori
PA|ϕ > (an ) =|< an | ϕ >|2
< A >|ϕ > =< ϕ | A | ϕ >
∆ |ϕ > A = < ϕ | A2 | ϕ > − < ϕ | A | ϕ > 2
2
La simulació....
PS x |S z , + > (+h / 2) =|< S x ,+ | S z ,+ >|2 = 1 / 2
< S x >|S z , + > =< S z ,+ | S x | S z ,+ >= 0
| S z ,+ > →
∆ |S z , x > S x = < S z ,+ | S x2 | S z ,+ > − < S z ,+ | S x | S z ,+ > 2 = h / 2
PS x |S z , + > (−h / 2) =|< S x ,− | S z ,+ >|2 = 1 / 2
h
2
h
2
µ = 4982 − 5018 = −0.0036
h
2
2
h
 h  4982 + 5018
− µ2 ≈
10000
2
2
σ=  
1

h
 − 0.0036 ±

10000  2

Spin 1/2
d̂
 cos(θ / 2) 

| S dˆ ,+ >=  iφ
e
sin(
θ
/
2
)


 − e −iφ sin(θ / 2) 

| S dˆ ,− >= 

 cos(θ / 2) 
3
observables
− iφ
h  cos(θ ) e sin(θ ) 

S dˆ =  iφ
2  e sin(θ ) − cos(θ ) 
Spin 1
 cos (θ / 2) 


| S dˆ ,1 >=  e iφ sin(θ ) / 2 
 e 2iφ sin 2 (θ / 2) 


2
 − e −iφ sin(θ ) / 2 


| S dˆ ,0 >= 
cos(θ )


 iφ
e
sin(
θ
)
/
2


1
2
 (−1 + cos(θ ))(i cos(φ ) + sin(φ )) 

2
| S dˆ ,−1 >= 
− e −iφ sin(θ ) / 2

2


cos (θ / 2)




4
Observable

cos(θ )

S dˆ = h e iφ sin(θ ) / 2

0

|
e − iφ sin(θ ) / 2
0
e iφ sin(θ ) / 2

0

− iφ
e sin(θ ) / 2 

− cos(θ ) 
Simulacions per spin 1/2
θ = φ = 450
5
Simulacions per spin 1
θ = φ = 450
6