# Questions tagged [matrix-elements]

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### Proving that a matrix consisting of the eigenvectors of a two-state system can simplify the Hamiltonian

I am at the late undergrad level. My professor has asked me to use the matrix $U=\left( {\begin{array}{cc} u & -v \\ v & u \\ \end{array} } \right)$ to simplify the Hamiltonian like ...
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### Derivation of equivalence of molecular and atomic orbitals

Intuitively, it seems quite reasonable that n atomic orbitals produce n molecular orbitals. I'm curious about how this can be proven from the generalised eigenvalue equation for the AO coefficients. ...
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1 vote
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### Matrix Elements of the raising and lowering operators for angular momentum

I was taught in our chemistry spectroscopy class (NMR module) that the matrix elements of $J_+$ and $J_-$ operators are respectively $\sqrt{(s-m)(s+m+1)}\hbar$ and $\sqrt{(s+m)(s-m+1)}\hbar$, but the ... 154 views

### Kronecker Delta to Matrix form of operator

I've recently seen the expression of the creation and annihilation operator in the harmonic oscillator in terms of matrices. What I've understood is that: $$A_{ij} = \langle i | A | j\rangle.$$ ...
161 views

### Derivative of eigenvalues with respect to parameter

By trying to find precise ways to calculate the derivative of numerical Hermitian matrices, I've recently stumbled upon this post in Math Stack Exchange. From the first answer on that post we get an ...
1 vote
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### Definitions of Determinants and Permanents in QFT

I have been recently reading a QFT book called: "QFT For the Gifted Amateur". It states in footnote 4 on p. 40 that the determinants and permanents of matrices can be defined as follows:  \...
65 views

### Summing of neutrino spins in Muon decay

This might be a silly question, but I am just a beginner so please bear with me. When we average the matrix element over spins, do we also have to sum over neutrino spins since neutrinos are only Left-...