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# Questions tagged [matrix-elements]

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### When Eigenfunctions/Wavefunctions are real?

When the Hamiltonian is Hermitian(i,e. beyond the effective mass approximation), generally under which conditions the eigenfunctions/wavefunctions are real? What happens in 1D case like the finite ...
2k views

218 views

### How to derive the Schrödinger Equation from Heisenberg's matrix mechanics and vice-versa?

How do you derive the Schrödinger equation (wave mechanics, time dependent state) from Heisenberg's Matrix Mechanics (matrix based, time dependent operators)
969 views

### Vector space of $\mathbb{C}^4$ and its basis, the Pauli matrices

How do I write an arbitrary $2\times 2$ matrix as a linear combination of the three Pauli Matrices and the $2\times 2$ unit matrix? Any example for the same might help ?
198 views

### How is simple matrix representation related to quantum probabilities?

I went again through some of my undergraduate books of quantum mechanics to get a new look at it as a futur PhD (not in QM though). I got answers for some old questions that bugged me at the time but ...
113 views

### PDFs expressed through matrix elements of bi-local operators

Extracted from 'At the frontier of ParticlePhysics, handbook of QCD, volume 2', '...in the physical Bjorken $x$-space formulation, an equivalent definition of PDFs can be given in terms of matrix ...
764 views

### How to construct the matrix of Hamiltonians for a hexagonal lattice

For part of a project I need to solve the time-independent Schrödinger equation, $\mathbf H\Psi = E\Psi$ (where $\mathbf H$ is the matrix with elements $\langle\Psi_i|H|\Psi_j\rangle$, and $\mathbf S$ ...
The usual matrix form of an operator $X$ is given by matrix components $$\langle a''| X | a' \rangle$$ where $|a' \rangle$ forms a basis for the ket space. In the case where we define matrix of ...
Consider the next matrix: M_{ab} = \left(\begin{array}{cccc} -1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ \end{array}\...