What are Eigenkets and Eigenvectors and how do they relate to quantum mechanics?

[sol66]

Ok I understand how to find eigenvectors, but I don't understand what they are. I am also uneasy with eigenkets and I don't understand what they are also. I need to understand both these topics to get a grasp on quantum mechanics. thank you

 

[CompuChip]

The last question is just a matter of language. Basically, a ket is a vector in a particular vector space called Hilbert space, in which (classes of) vectors represent physical states. Thus, if you read "ket" for "vector" your question reduces again to "what are eigenvectors?".

Let me first ask you some preliminary questions.

How firm is your knowledge of linear algebra? Do you know what eigenvectors are in that context?
Have you ever heard about the interpretation of a matrix as representation of a linear map between vector spaces?

 

[jegues]

Eigenvectors in terms of geometrical signficance are vectors in which the direction is either preserved or reversed and the magnitude of the vector is either stretched, compressed or unchanged.

 

[sol66]

Well I have not taken a formal course in linear algebra and the math methods course that was suppose to teach me this only showed me how to solve for these things and not how to interpret it. I don't know what you mean by interpreting a matrix as a linear map between vector spaces, however I have heard that that vectors are mapped onto operating matrices.

This is my understanding so far, given that you use eigenvalues to diagnolize a matrice, once you find your values you can then find a vector which is preserved in direction whenever your operator acts on that vector. That vector that has a preserved direction given your matrice operator is called your eigenvector.

Please let me know if my understanding is correct

 

[jegues]

which is preserved in direction

To be more specific it conserves its direction along a particular line.

Since you can reverse its direction, it's not necessairly pointing in the same direction, but pointing in a direction along the same line.