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Consider two electrons in a singlet state (total spin = 0). (a) If a measurement of the spin of one of the electrons reveals it is in a state with sz = +ħ/2, what is the probability that a measurement of the z-component of the spin of the other electron yields +h/2? (b) A measurement of the spin of both electrons (in the singlet state) is made simultaneously as follows: for one electron, the spin orientation is measured in the z-direction, while for the other electron it is made in the x-direction. If the measurement of sz reveals that the electron is in a state with sz = +ħ/2, what is the probability that the measurement of the x-component of the spin of the other electron yields S = +h/2?

Consider two electrons in a singlet state (total spin = 0). (a) If a measurement of the spin of one of the electrons reveals it is in a state with sz = +ħ/2, what is the probability that a measurement of the z-component of the spin of the other electron yields +h/2? (b) A measurement of the spin of both electrons (in the singlet state) is made simultaneously as follows: for one electron, the spin orientation is measured in the z-direction, while for the other electron it is made in the x-direction. If the measurement of sz reveals that the electron is in a state with sz = +ħ/2, what is the probability that the measurement of the x-component of the spin of the other electron yields S = +h/2?

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Q2.2) Answer question completely and with much detail as possible. Need to understand the concept.
Consider two electrons in a singlet state (total spin = 0). (a) If a measurement of the spin of one of the electrons reveals it is in a state with sz = +ħ/2, what is the probability that a measurement of the z-component of the spin of the other electron yields +ħ/2? (b) A measurement of the spin of both electrons (in the singlet state) is made simultaneously as follows: for one electron, the spin orientation is measured in the z-direction, while for the other electron it is made in the x-direction. If the measurement of sz reveals that the electron is in a state with sz = +ħ/2, what is the probability that the measurement of the r-component of the spin of the other electron yields Sz = +ħ/2?
Transcribed Image Text:Consider two electrons in a singlet state (total spin = 0). (a) If a measurement of the spin of one of the electrons reveals it is in a state with sz = +ħ/2, what is the probability that a measurement of the z-component of the spin of the other electron yields +ħ/2? (b) A measurement of the spin of both electrons (in the singlet state) is made simultaneously as follows: for one electron, the spin orientation is measured in the z-direction, while for the other electron it is made in the x-direction. If the measurement of sz reveals that the electron is in a state with sz = +ħ/2, what is the probability that the measurement of the r-component of the spin of the other electron yields Sz = +ħ/2?
Expert Solution
Step 1

Given,

Two electrons are in a singlet state so their total spin will be zero.

And the state vector for these two electrons will be

|ψ>=12ϕ1↑ϕ2↓-ϕ1↓ϕ2↑|ψ>=12|12,12> |12,-12>  -  |12,-12> |12,12>

Here,

|eigenstate of Sz,eigenvalue±h2> 

 

a)

According to the question, both electrons have the same eigenvalue or both have +h2 of the state. And from Pauli exclusion principle no two electrons can present in a same state having same same spin. 

So the probability of electrons to find in the same state will be zero.

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