# Questions tagged [eigenvalue]

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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### Energy eigenvalue with Potential $-e^2/ x$

If I have potential which are very well-known like, square barrier, or square well, or step potential, What I do is to set the boundary conditions in Schrödinger's equations. Sometime, the ground ...
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### For vibrations in continuous beam, what is the unit of eigenvalue?

I have been solving a fourth order euler bernoulli differential equation to solve for vibrations of a continuous cantilever beam. When I verified for them using Comsol eigenvalue solver, it gives me ...
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### Different formula to find $2\times 2$ Hamiltonian's eigenvalues [closed]

Consider the Hamiltonian $$\left[ \begin{matrix} E_1 & -A\\ -A& E_2\\ \end{matrix} \right]$$ where $A$, $E_1,E_2$ are real numbers. I have seen a different formula to ...
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### Eigenvectors of the BCS Hamiltonian

In introductory superconductivity one often studies the BCS Hamiltonian $$H= \begin{pmatrix} \xi & -\Delta \\ -\Delta & -\xi \end{pmatrix}$$ I can find the Eigenvalues and Eigenvectors by ...
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Can an arbitrary many-body hamiltonian in second quantization form with quadratic and biquadratic terms $$H=\sum_{v_1,v_2} \alpha_{v_1 v_2}\ c_{v_1}^{\dagger}c_{v_2}+ \sum_{v_1,v_2,v_3,v_4}\beta_{v_1 ... 1answer 85 views ### Wigner proof of the non-existence of finite unitary representation of the Lorentz group I am reading Wigner's paper ”On unitary representations of the inhomogenous Lorentz group” (Annals of Mathematics, Vol. 40, No.1, p. 149) found here: https://www.maths.ed.ac.uk/~jmf/Teaching/Projects/... 1answer 47 views ### What do I get by multiplying a 0 operator on a 0 eigenvector? I don't know how to write the equation form. Assuming my notation as Dirac notation, what do I get from$$ ( 0 | 0 | 0 ) ~?$$1answer 726 views ### What is eigenvalue and eigenfunction in quantum mechanics? What is the use of eigenvalue and eigenfunction in quantum mechanics specially Schrodinger equation? What is the physical meaning of having an eigenvalue and eigenfunction in Schrodinger equation? 1answer 78 views ### Energy of Free-electron Gas - Landau Levels in 3D so i am looking into Landau Diamagnetism and am reading Dupre's paper. I am slightly confused at where he has got a term in his value of E from. He states that:$$ E=(n+1/2)\hbar\omega+\hbar^2k_z^...
I'm studying the quantum Ising model, i.e. with Hamiltonian $H= -h\sum_{i}X_i-\sum_{\langle i,j\rangle}Z_iZ_j$. I know conceptually how to compute the ground state of the Ising model at zero ...