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Consider the system given by, $$ H|n\rangle = E|n\rangle$$ where: $H$ is the hamiltonian. $|n\rangle$ is the eigenstate. $E$ is the energy of the eigenstate. Now from non-degenerate perturbation ...

first, I have a general question. In perturbation theory, I saw perturbations in eigenvalues and eigenvectors of square, non-symmetric matrices and the calculations were all right but no one ever ...

(I understand this question might not be appropriate for this website, but it has been asked on MathStackexchange and did not receive any replies even with a bounty) How can I prove that the ...

Theorem (Rellich). Let $\boldsymbol{A}(t) : \mathbb{R}\rightarrow\mathbb{C}^{n \times n}$ be a Hermitian matrix function that depends on $t$ analytically. (i) The $n$ roots of the characteristic ...

Consider a matrix function $A(x)$, analytically depending on single parameter $x$. Consider the eigenvalue/eigenvector pair of $A(0)$, namely $\lambda(0)$ and $w(0)$. The question is whether we can ...