Find Eigenvalue: Solutions for Beginners

  • Thread starter stagger_lee
  • Start date
  • Tags
    Eigenvalue
In summary, the conversation is about finding the corresponding eigenvalue for an eigenfunction of the operator d^2/dx^2, which is given as ψ = e^2x. The person asking for help has no experience in Physics and is struggling with the problem. They have provided the necessary information, such as the homework statement, equations, and their attempt at a solution. They have also been directed to read an article on eigenvectors as a starting point.
  • #1
stagger_lee
14
0
Hi all, any help greatly appreciated.

Please bear in mind that i have no experience in any Physics and genuinly have no idea how to these questions.


Homework Statement



An eigenfunction of the operator d^2/dx^2 is ψ = e^2x. Find the corresponding eigenvalue.


Homework Equations





The Attempt at a Solution

 
Physics news on Phys.org
  • #2
stagger_lee said:
Hi all, any help greatly appreciated.

Please bear in mind that i have no experience in any Physics and genuinly have no idea how to these questions.


Homework Statement



An eigenfunction of the operator d^2/dx^2 is ψ = e^2x. Find the corresponding eigenvalue.


Homework Equations





The Attempt at a Solution


Good Afternoon Stagger,

Please read this article as a start: http://en.wikipedia.org/wiki/Eigenvector
 

FAQ: Find Eigenvalue: Solutions for Beginners

1. What is an eigenvalue?

An eigenvalue is a numerical value that represents a scalar factor by which a vector is scaled when a linear transformation is applied to it. In simpler terms, it is a value that describes how a vector changes when it is transformed.

2. How do you find eigenvalues?

To find eigenvalues, you first need to find the characteristic polynomial of the matrix. This is done by subtracting the identity matrix multiplied by a scalar from the original matrix and setting the determinant equal to zero. The solutions to this polynomial are the eigenvalues.

3. What is the importance of eigenvalues?

Eigenvalues are important in many fields, including physics, engineering, and computer science. They are used to analyze and understand linear transformations, such as those found in systems of differential equations and in data analysis techniques like principal component analysis.

4. Can matrices have more than one eigenvalue?

Yes, matrices can have multiple eigenvalues. In fact, most matrices have more than one eigenvalue. The number of distinct eigenvalues a matrix has is equal to its size. For example, a 3x3 matrix can have up to 3 distinct eigenvalues.

5. How are eigenvalues and eigenvectors related?

Eigenvalues and eigenvectors are closely related. Eigenvectors are the corresponding vectors that are scaled by the eigenvalue when a linear transformation is applied. In other words, an eigenvector is a vector that does not change direction when multiplied by the matrix. Eigenvalues and eigenvectors are used together to understand and analyze linear transformations.

Similar threads

Why Are My Coupled Oscillator Eigenvalues Incorrect?
Replies
6
Views
1K
Finding eigenvalue energy between two spheres
Replies
1
Views
1K
Correct Setup for Finite Difference to Calculate Quantum Tunneling
Replies
2
Views
443
Ground state energy eigenvalue of particle in 1D potential
Replies
6
Views
2K
Eigenvalues and eigenkets of a two level system
Replies
4
Views
2K
Show that the two wave functions are eigenfunction
Replies
1
Views
3K
Eigenvalues and eigenvectors of a Hamiltonian
Replies
2
Views
3K
Quantum mechanics - Heisenberg picture
Replies
1
Views
1K
Momentum eigenvalues and eigenfunctions
Replies
2
Views
1K
A The eigenvalue power method for quantum problems
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top