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Calculating Eigenkets of Perturbed Matrix for Second-Order Correction

While the equation for the second-order correction \begin{equation} E_n^{(2)} = \langle n^0 | H^1 | n^1 \rangle \end{equation} Is correct, I found that it is more useful to put that equation in its ...
PineappleThursday's user avatar
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Numerical solution to Schrödinger equation - eigenvalues

The “phase method” http://gbxafs.iit.edu/phase-method/ easily solves it. It’s new. Take a look.
user403303's user avatar
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Different definitions of resolvent in matrix model

For what it's worth, averaging/integrating over $M$ $$\langle\ldots \rangle$$ produces different quantities: Before the quantity depends on a matrix $M$ (or at least its eigenvalues, due to the ...
Qmechanic's user avatar
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Different definitions of resolvent in matrix model

This is due to self-averaging properties in the thermodynamic limit. It's a more involved case of the law of large numbers. Recall that for the latter, say you have integrable iid random variables $(...
LPZ's user avatar
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How to find eigenvalues and eigenvectors of the superoperator from those of the jump operator?

If $L$ is normal, i.e. $L=\sum_j\lambda_j|r_j\rangle\langle r_j|$, then the eigenvalues of your $\mathcal L$ are given by $$ -\frac12|\lambda_j|^2-\frac12|\lambda_k|^2+\overline{\lambda_j}\lambda_k $$ ...
Frederik vom Ende's user avatar
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Why does applying Ladder operators change the eigenfunction?

Surely an operator acting on an eigenfunction should spit out the exact same function multiplied by the corresponding eigenvalue? This is only true for the operator for which the function is an ...
Níckolas Alves's user avatar

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