QM Measurement Problem: Expectation Value of Lz

  • Thread starter y.moghadamnia
  • Start date
  • Tags
    Measuring
In summary, the conversation covers a question about the expectation value of Lz in a state where Lx=1. The speaker does not understand how knowing Lx can help calculate the expectation value of Lz and seeks advice on how to approach the problem. They mention studying the postulates of QM and asking others for practice problems, but have not received any responses.
  • #1
y.moghadamnia
23
1
hi there,
I have been studying the postulates of QM in shankar book, and in the part it explains how measurement affects the system, it talks alittle about the expectation value and the uncertainty. then I came across this problem which I don't get. it gives three L(in x direcion), L(in y direction) and L(in z direction) matrices and then asks " take the state in which Lx=1. In this state what is the expectation value of Lz?" I don't understand this part:
how knowing Lx can help us calculate the expectation value of Lz?
 
Physics news on Phys.org
  • #2
Given the matrix that represents Lx, you can write down the unique vector (up to a phase factor) that is an eigenvector of Lx with eigenvalue 1. Then you can calculate the expectation of Lz for this eigenvector.
 
  • #3
aha, so that's the way u got to look at it. guess I should solve more problems to understand the way of looking at the problems.I asked people if they had good problems to send me but no one answered.
 

Related to QM Measurement Problem: Expectation Value of Lz

1. What is the QM Measurement Problem?

The QM Measurement Problem is a fundamental issue in quantum mechanics that concerns the interpretation of measurement results in the theory. It arises from the fact that, according to quantum mechanics, the act of measurement can fundamentally alter the state of a system, making it difficult to reconcile with our classical understanding of measurement.

2. What is the Expectation Value of Lz?

The Expectation Value of Lz, also known as the z-component of angular momentum, is a quantum mechanical quantity that represents the average value of the measurement of angular momentum along the z-axis in a specific quantum state. It is a mathematical representation of the most likely outcome of a measurement of angular momentum in a given state.

3. How is the Expectation Value of Lz calculated?

The Expectation Value of Lz is calculated by taking the inner product of the quantum state with the operator for the z-component of angular momentum, and then squaring the result to obtain the average value. In mathematical terms, it can be represented as <Lz> = <ψ|Lz|ψ>, where <ψ| represents the bra vector, and |ψ> represents the ket vector of the quantum state.

4. What does the Expectation Value of Lz tell us about a quantum state?

The Expectation Value of Lz provides information about the distribution of angular momentum in a quantum state. It can tell us the most likely direction and magnitude of angular momentum if we were to perform a measurement on the state. It also helps us understand the uncertainty in the measurement of angular momentum, as the value can vary depending on the state of the system.

5. How does the Expectation Value of Lz relate to the QM Measurement Problem?

The Expectation Value of Lz is an important concept in understanding the QM Measurement Problem because it represents the average value of a measurement in quantum mechanics. It helps us understand why the act of measurement can be problematic in quantum mechanics and how it differs from our classical understanding of measurement. By studying the expectation value, we can better understand the implications of measurement in quantum mechanics.

Similar threads

I Why “If Lz has a well-defined value, then Lx and Ly do not”？
    • Quantum Physics
Replies
6
Views
2K
I Spin expectation value for one particle vs actual measurement
    • Quantum Physics
Replies
4
Views
1K
I Question about Stern-Gerlach experiment
    • Quantum Physics
Replies
12
Views
2K
I Measurements and uncertainty principle
    • Quantum Physics
Replies
12
Views
846
B Extremely elementary questions about QM
    • Quantum Physics
Replies
24
Views
2K
I von Neumann Measurement Scheme
    • Quantum Physics
Replies
2
Views
122
How to Calculate <Ly^2> Without Using Symmetry?
    • Advanced Physics Homework Help
Replies
6
Views
1K
I Second Matrices from Spherical Harmonics with Eigenvalue l+1
    • Quantum Physics
Replies
8
Views
1K
I Measurement problem - will this work?
    • Quantum Physics
Replies
3
Views
625
I Motivation behind the Operator-Formalism in QM
    • Quantum Physics
Replies
3
Views
535

Hot Threads

Recent Insights

Back
Top