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A linear operator (including a matrix) acting on a non-zero *eigenvector* preserves its direction but, in general, scales its magnitude by a scalar quantity *λ* called the *eigenvalue* or characteristic value associated with that eigenvector. Even though it is normally used for linear operators, it may also extend to nonlinear operations, such as Schroeder functional composition, which evoke linear operations.

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The eigenvalues of quantum harmonic oscillator [closed]

Can someone explain to me what is the green curve in the graphical rapresentation of energy levels for a quantum harmonic oscillator? I've always encounter this type of photo and nobody explains what …
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Trouble understing a passage from Principles of quantum mechanics by Paul Dirac?

I'm currently reading Principles of Quantum Mechanics by Paul Dirac, specifically the 4th edition of 1958. There is a passage I'm having trouble to understand, I'll put the text here. For reference it …
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Eigenvalues of Cooper Pair Box with Matlab

I wanted to evaluate the eigenvalues of the Cooper Pair Box Hamiltonian in number basis $$ \hat H=\sum_n 4E_c(n-n_g)^2 |n\rangle\langle n|-E_J/2(|n\rangle\langle n+1|+|n+1\rangle\langle n|) $$ as a fu …
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