Measurement of Lx: Result of Measurement?

[Physgeek64]

Homework Statement

If we have a wave function $\psi =zf(r)$ and we take a measurement of $L_x$ what is the result of the measurement?

Homework Equations

The Attempt at a Solution

So i know we can write $L_x=\frac{1}{2}(L_+ + L_- )$ and that $|\psi > = g(r) |1,0>$ so $L_x |\psi >= \frac{1}{2} \sqrt{2} g(r) |1,1>$. But i don't know what the measurement would be because this has to be an eigenvalue equation to read off the result of a measurement (I think?).

Many thanks!

 

[drvrm]

The Attempt at a Solution

So i know we can write Lx=12(L++L−)Lx=12(L++L−)L_x=\frac{1}{2}(L_+ + L_- ) and that |ψ>=g(r)|1,0>|ψ>=g(r)|1,0>|\psi > = g(r) |1,0> so Lx|ψ>=12√2g(r)|1,1>Lx|ψ>=122g(r)|1,1>L_x |\psi >= \frac{1}{2} \sqrt{2} g(r) |1,1>. But i don't know what the measurement would be because this has to be an eigenvalue equation to read off the result of a measurement (I think?).

Many thanks!

you have a given wave function which is a function of r and theta only
if you wish to find expected value of L(x) then one must use differential form of the operator L(x)

 

[Physgeek64]

you have a given wave function which is a function of r and theta only
if you wish to find expected value of L(x) then one must use differential form of the operator L(x)

But how do i find the result of a measurement. I can show that the expected value is zero, but i don't know what the outcome of an individual measurement would be.

 

[drvrm]

But how do i find the result of a measurement. I can show that the expected value is zero, but i don't know what the outcome of an individual measurement would be.

In QM the measurement is defined with the help of wave function
say you have a position wavefunction then you can measure x-operator

as {Psi * (x )Psi }integrated over the whole space.
similarly L(x) is a operator which is represented in (r,theta, phi) space .

put the complex conjugate of the wave function on the left and psi on the right and L(x) in between and integrate over whole space .
the result will give you measurement and it may not be zero.