Schrödinger Equation

iℏ∂∂tΨ(r,t)=[−ℏ22m∇2+V(r,t)]Ψ(r,t)i\hbar\frac{\partial}{\partial t}\Psi(\mathbf{r},t) = \left[-\frac{\hbar^2}{2m}\nabla^2 + V(\mathbf{r},t)\right]\Psi(\mathbf{r},t)iℏ∂t∂​Ψ(r,t)=[−2mℏ2​∇2+V(r,t)]Ψ(r,t)

Fourier Transform

f^(ξ)=∫−∞∞f(x) e−2πixξ dx\hat{f}(\xi) = \int_{-\infty}^{\infty} f(x)\,e^{-2\pi i x\xi}\,dxf^​(ξ)=∫−∞∞​f(x)e−2πixξdx

Einstein's Field

Gμν+Λgμν=8πGc4TμνG_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4}T_{\mu\nu}Gμν​+Λgμν​=c48πG​Tμν​

Riemann Hypothesis

ζ(s)=∑n=1∞1ns\zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s}ζ(s)=∑n=1∞​ns1​

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