Stern-Gerlach experiment Problem

[BREAD]

Homework Statement

Homework Equations

The Attempt at a Solution

(a) : There is no interference. (b) : Interference

And i don't know how to approach (c), (d)

 

[kuruman]

And i don't know how to approach (c), (d)

Consider the wavefunctions in each case and the probability distribution at the screen that they entail.

 

[BREAD]

Consider the wavefunctions in each case and the probability distribution at the screen that they entail.

(c) is just sum of l+> + l-> so the answer is same with (b), and i don't know if there is interference between l+> and l+>

 

[kuruman]

is just sum of l+> + l->

In case (c), if you were to measure an electron's spin with another Stern-Gerlach machine, would you be able to tell through which slit the electron emerged?
What about if you did the same with an electron in case (d)?

 

[BREAD]

In case (c), if you were to measure an electron's spin with another Stern-Gerlach machine, would you be able to tell through which slit the electron emerged?
What about if you did the same with an electron in case (d)?

I think , in case of (c) , there would be same amount of electron goes through each slit.

 

[kuruman]

think , in case of (c) , there would be same amount of electron goes through each slit.

My question to you was not about amounts of electrons.
1. Suppose in case (c) you measured the spin of an electron to the right of the slits and you found it is "up". Would you be able to tell through which slit it went through?
2. Suppose in case (d) you measured the spin of an electron to the right of the slits and you found it is "up". Would you be able to tell through which slit it went through?

 

[BREAD]

My question to you was not about amounts of electrons.
1. Suppose in case (c) you measured the spin of an electron to the right of the slits and you found it is "up". Would you be able to tell through which slit it went through?
2. Suppose in case (d) you measured the spin of an electron to the right of the slits and you found it is "up". Would you be able to tell through which slit it went through?

up spin go through upper slit

and in (d), up spin would be found in both slits

 

[kuruman]

So in (c) you know through which slit the electrons have passed through, but in (d) you do not know. Can you put it together now in view of your answers in (a) and (b) and what you know about quantum interference?

 

[BREAD]

So in (c) you know through which slit the electrons have passed through, but in (d) you do not know. Can you put it together now in view of your answers in (a) and (b) and what you know about quantum interference?

I think in (c), upper slit ( + ) and lower slit ( - ) will interfere each other, and similarly, upper slit (+) and lower slit(+) will interfere each other in (d).
Or do i have to focus on that l+> and l-> are independent each other, so there are no interfere between l+> and l-> ??

 

[kuruman]

Please read about "which way" experiments here.
https://en.wikipedia.org/wiki/Double-slit_experiment

 

[BREAD]

I think i get it , this is my answer

But, is it right that i have to draw a half intensity in (c),(d) compared to (a),(b)

 

[kuruman]

But, is it right that i have to draw a half intensity in (c),(d) compared to (a),(b)

It's not a matter of intensity. If the electron flux is the same in all four cases, then what do you think should be the same in all four graphs?