Live mathematical reference

Mathematical compendium

A live index of the equations in published articles. Each entry leads to its article, equation guide, and the terms explained there. New or edited published articles appear automatically.

1709 equations across 1439 symbols.

keff=2(2π/589 nm)=2.1335×107 m−1k_{\rm eff}=2(2\pi/589\,\mathrm{nm})=2.1335\times10^{7}\,\mathrm{m^{-1}}

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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mop[LG]=ℏ Φ[LG]b⋅vm_{\rm op}[\mathcal L_{\rm G}]=\frac{\hbar\,\Phi[\mathcal L_{\rm G}]}{\mathbf b\cdot\mathbf v}

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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mop=ℏc2 ∂Δϕ∂Δτ,mop[LG]=ℏ ∂Φ∂(b⋅v)m_{\rm op}=\frac{\hbar}{c^2}\,\frac{\partial\Delta\phi}{\partial\Delta\tau},\qquad m_{\rm op}[\mathcal L_{\rm G}]=\hbar\,\frac{\partial\Phi}{\partial(\mathbf b\cdot\mathbf v)}

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

All uses →Latest guide →Latest article →