How to Find the Final State and Probability After Measuring \(L_x^2\)?

AI Thread Summary
To find the final state after measuring \(L_x^2\) and obtaining a result of 0, the initial state in the \(L_z\) basis must be expressed in terms of the eigenstates of \(L_x\). The measurement collapses the state to the corresponding eigenstate of \(L_x\) associated with the eigenvalue of 0. The probability of obtaining this result can be calculated by projecting the initial state onto the eigenstate of \(L_x\) that corresponds to the measured value. The discussion highlights the need to clarify the relationship between the states in different bases and the process of measurement in quantum mechanics. Understanding these concepts is crucial for accurately determining the final state and its probability.
liorda
Messages
28
Reaction score
0

Homework Statement



consider the state (\frac{1}{2}, \frac{1}{2}, \frac{1}{\sqrt{2}}) in L_z basis. If L_x^2 is measured and the result of 0 is obtained, find the final state after the measurement. How probable is this result?

The Attempt at a Solution



I'm not sure if the state is superposition of the known ground states of L_x in L_z representation. How to find the state of the system after the measurement? And should I sum the probabilities of getting each of that state eigenvalues?

thanks.
 
Physics news on Phys.org
any moderator, please move my question to quantum physics forum. thanks.
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Measurement of Lx: Result of Measurement?
Replies
3
Views
1K
Help Calculating probability between 2 limits for the ground state
Replies
28
Views
1K
Solve L=2 Atom Problem: Find Min (L_x)^2 + (L_y)^2
Replies
1
Views
1K
I Writing the wave function solutions for a particle in a 2-D box
Replies
1
Views
1K
Probability of Measuring ##L_x = 0## for a Given ##\psi##
Replies
4
Views
2K
What is the problem with the units in this state equation of a gas?
Replies
12
Views
1K
Difference between stationary/non-stationary quantum states
Replies
6
Views
6K
Mixing two gases in an isolated system and calculating final p and T
Replies
4
Views
2K
Question about the superposition of energy states
Replies
11
Views
3K
2 Masses and a Wheel (with mass)
Replies
6
Views
758

Hot Threads

Recent Insights

Back
Top