Finding Quantum Numbers and Eigenvectors from Matrices A & B

In summary, The conversation discusses finding the quantum numbers and eigenvectors for matrices A and B that commute. The speaker has solved the problem by combining unique pairs of eigenvalues and determining an eigenvector that fulfills both A and B's constraints.
  • #1
greisen
76
0
Hey,

I have two matrices A and B which commute. For A I have 1,-1,-1 and for B I have 1,2,2.

I am asked to find the quamtum number for the three states. How to find the quantum states from the eigenvalues. It is further said that it is possible to find the eigenvectors from the quantum numbers. How to get the eigenvector from the quantum numbers?

Any help appreciated - thanks in advance
 
Physics news on Phys.org
  • #2
I think I have solved it by combining the three pairs into unique pairs
{1,1},{2,1},{2,-1} having these constraints on the eigenvector equation it is possible to determine a eigenvector for the matrix A fulfilling both A and B.
 

1. How do I find the quantum numbers from a given matrix A?

The quantum numbers correspond to the eigenvalues of matrix A. To find the eigenvalues, you can use the characteristic polynomial and solve for the roots. These roots will be the quantum numbers.

2. Can I use matrix B to find the quantum numbers?

No, the quantum numbers are only found in matrix A. Matrix B may have different eigenvalues and eigenvectors, but they do not correspond to the quantum numbers.

3. How do I find the eigenvectors from matrices A and B?

The eigenvectors can be found by solving the eigenvalue equation Ax = λx, where x is the eigenvector and λ is the corresponding eigenvalue. This equation can be solved by using Gaussian elimination or other methods.

4. Can I use a calculator or computer program to find the quantum numbers and eigenvectors?

Yes, there are many programs and calculators that can help you find the eigenvalues and eigenvectors of a matrix. However, it is important to understand the mathematical concepts behind these calculations in order to properly interpret the results.

5. What is the significance of finding quantum numbers and eigenvectors from matrices A and B?

Finding the quantum numbers and eigenvectors from matrices A and B can help us understand the properties and behavior of quantum systems. These numbers and vectors provide information about the energy levels and allowed states of a quantum system, and can be used in various calculations and analyses.

Similar threads

How to find the eigenvector for a perturbated Hamiltonian?
    • Advanced Physics Homework Help
Replies
13
Views
1K
Two-level Quantum System - initial state
    • Advanced Physics Homework Help
Replies
14
Views
1K
Eigenvalues and eigenvectors of J3
    • Advanced Physics Homework Help
Replies
17
Views
1K
A Finding Eigenvectors for Two Matrices using the Generalized Jacobi Method
    • Linear and Abstract Algebra
Replies
7
Views
980
What are energy values and how do they relate to eigenvectors in quantum states?
    • Advanced Physics Homework Help
Replies
17
Views
2K
Commutation and Measurement of Observables
    • Advanced Physics Homework Help
Replies
4
Views
1K
Analysing the Normal Modes and Dynamics of a Cluster of Atoms
    • Advanced Physics Homework Help
Replies
1
Views
916
Particle in a cylindrically symmetric potential (Quantum mechanics)
    • Advanced Physics Homework Help
Replies
5
Views
1K
I How are good quantum numbers related to perturbation theory?
    • Quantum Physics
Replies
18
Views
2K
Find the eigenvector with zero eigenvalues at any time t from the Hamiltonian
    • Advanced Physics Homework Help
Replies
1
Views
986

Hot Threads

Recent Insights

Back
Top