# Probability of Negative Value in Sz 1/2 Spin System w/ Lambda 1 & 2

• ellenb899
In summary, the question asks for the probability of measuring a negative value for the spin state of a Sz 1/2 spin system, given a wavefunction in bra-ket notation with eigenvalues of lambda 1 = hbar/2 and lambda 2 = -h bar/2. Based on the given information, it can be determined that a negative value cannot be obtained as it must be squared, and the probability of measuring a spin-down state is dependent on the coefficients of the wavefunction. Additionally, it is recommended to use LaTeX for writing mathematical equations for better readability.
ellenb899
Homework Statement
Will the probability to provide a negative value of a Sz 1/2 spin system always be 0? If lambda 1 = hbar/2 and lambda 2 = -h bar/2 ?
Relevant Equations
P1(Sz = hbar/2) = |c1|^2
Will the probability to provide a negative value of a Sz 1/2 spin system always be 0? If lambda 1 = hbar/2 and lambda 2 = -h bar/2 ?

The question is not clear. Can you post the full statement?

Also, PhysicsForums requires you to provide an attempt at a solution.

vanhees71
Given particle in spin state: wavefunction in bra-ket notation = 3N|1> + i4N|2> (1/2 spin state in z axis)

Q. What is the probability that a measurement of Sz will provide negative value?

My attempt at solution is using the equation I provided, a negative value cannot be obtained as it must be squared. Is this correct?

Probabilities are always positive or zero, but it has nothing to do with the sign of what will be measured.

In other words, the question asks for the probability of measuring the spin as spin-down.

ellenbaker said:
Given particle in spin state: wavefunction in bra-ket notation = 3N|1> + i4N|2> (1/2 spin state in z axis)
I don't understand what the states ##\ket{1}## and ##\ket{2}## correspond to.

I guess you will also have to figure out what the value of ##N## is.

For a spin 1/2 the eigenvalues of ##\sigma_z## are ##\pm \hbar/2##. A general state is
$$|\psi \rangle = a |\hbar/2 \rangle+ b|-\hbar/2 \rangle, \quad |a|^2+|b|^2=1.$$
The probability to find ##+\hbar/2## when measuring ##\sigma_z## is
$$P(+\hbar/2)=|a|^2,$$
and the probability to find ##-\hbar/2## is
$$P(-\hbar/2)=|b|^2.$$
So what's the question?

PS: For writing readable math, it's most convenient to use LaTeX. Just check the "LaTeX Guide" link below the entry form:

https://www.physicsforums.com/help/latexhelp/

Replies
9
Views
913
Replies
5
Views
2K
Replies
9
Views
958
Replies
1
Views
429
Replies
1
Views
816
Replies
1
Views
1K
Replies
3
Views
901
Replies
1
Views
865