Measurement problem quantum mechanics

[Ashish Somwanshi]

Homework Statement

Measurement

Suppose an electron is in a spin state that can be described by

|ϕ⟩=3/√2|+⟩+1/2|−⟩
where + and – are eigenstates of Sz with eigenvalue +ℏ/2 and −ℏ/2.

If we measure z-component of spin of this electron, what is the probability of measuring spin up, +ℏ/2?

Answers within 5% error will be considered correct.

Relevant Equations

I myself want to know which formula we need to use.

I was not able to attempt since I don't know which formula or method can be used to solve the problem

 

[topsquark]

Homework Statement:: Measurement

Suppose an electron is in a spin state that can be described by

|ϕ⟩=3/√2|+⟩+1/2|−⟩
where + and – are eigenstates of Sz with eigenvalue +ℏ/2 and −ℏ/2.

If we measure z-component of spin of this electron, what is the probability of measuring spin up, +ℏ/2?

Answers within 5% error will be considered correct.
Relevant Equations:: I myself want to know which formula we need to use.

I was not able to attempt since I don't know which formula or method can be used to solve the problem

First you need to normalize the state.

Hint 1: What does the result of operating $S_z$ mean?

Hint 2: Once you have that, how can you find the probability of finding the electron in the $\mid + >$ state?

-Dan

 

[PeroK]

Homework Statement:: Measurement

Suppose an electron is in a spin state that can be described by

|ϕ⟩=3/√2|+⟩+1/2|−⟩

Is that supposed to be $\frac {\sqrt 3}{2}\ket + + \frac 1 2 \ket -$?

(Otherwise there is a rogue square root in the denominator!)

 

[topsquark]

First you need to normalize the state.

Hint 1: What does the result of operating $S_z$ mean?

Hint 2: Once you have that, how can you find the probability of finding the electron in the $\mid + >$ state?

-Dan

A quick note. I was looking at this wrong.

Correction:
Hint 1: How do we find the component of |+> from the ket?

Hint 2: How do we then find the probability it's in the |+> state from that?

-Dan

 

[DrClaude]

Born rule: the probability of measuring the system $\ket{\psi}$ in state $\ket{\alpha}$ is given by
$$
\mathcal{P}(\alpha) = \left| \braket{\alpha | \psi} \right|^2
$$