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## Main Question or Discussion Point

Hey guys (this is not a HW problem, just general discussion about the solution that is not required for the assignment),

So I am doing this problem where I had to find the eigenvalues and eigenvectors of the Hamiltonian:

H = A*S[itex]_{x}[/itex][itex]^{2}[/itex] + B*S[itex]_{y}[/itex][itex]^{2}[/itex] + C*S[itex]_{z}[/itex][itex]^{2}[/itex].

Easy enough, just basic linear algebra.

However, I want to interpret what the results I get. So I understand the eigenvalues of H represents the energy levels of the system but what physical interpretation should i take to the eigenvectors?

So by finding the eigenvectors, I find a basis that spans the space I am working in. Why is this important to know? I dont want to lose the forest for the trees and just trying to grapple with why the eigenvectors are important or what they physically mean? (eg energy levels have a physical meaning to me, so the eigenvalues make sense but the eigenvectors seem abstract to me). I know I should follow the math in QM but I like to understand the world, not just apply math tricks... Thanks!

So I am doing this problem where I had to find the eigenvalues and eigenvectors of the Hamiltonian:

H = A*S[itex]_{x}[/itex][itex]^{2}[/itex] + B*S[itex]_{y}[/itex][itex]^{2}[/itex] + C*S[itex]_{z}[/itex][itex]^{2}[/itex].

Easy enough, just basic linear algebra.

However, I want to interpret what the results I get. So I understand the eigenvalues of H represents the energy levels of the system but what physical interpretation should i take to the eigenvectors?

So by finding the eigenvectors, I find a basis that spans the space I am working in. Why is this important to know? I dont want to lose the forest for the trees and just trying to grapple with why the eigenvectors are important or what they physically mean? (eg energy levels have a physical meaning to me, so the eigenvalues make sense but the eigenvectors seem abstract to me). I know I should follow the math in QM but I like to understand the world, not just apply math tricks... Thanks!