jd7h
/
texify
Converts images or pdfs containing math into markdown and LaTeX that can be rendered by MathJax
Prediction
jd7h/texify:485f0de1ModelIDuuuqretbfauc3gl5vmdxg4ivwyStatusSucceededSourceWebHardwareA40Total durationCreatedInput
- image
- katex_compatible
Output
The potential $V_i$ of cell $\mathcal{C}_i$ centred at position $\mathbf{r}_i$ is related to the surface charge densities $\sigma_j$ of cells $\mathcal{C}_j$ $j\in[1,N]$ through the superposition principle as: $$V_i\,=\,\sum_{j=0}^{N}\,\frac{\sigma_j}{4\pi\varepsilon_0}\,\int_{\mathcal{C}_j}\frac{1}{\|\mathbf{r}_i-\mathbf{r}^{\prime}\|}\,\mathrm{d}^2\mathbf{r}^{\prime}\,=\,\sum_{j=0}^{N}\,Q_{ij}\,\sigma_j,$$ where the integral over the surface of cell $\mathcal{C}_j$ only depends on $\mathcal{C}_j$ shape and on the relative position of the target point $\mathbf{r}_i$ with respect to $\mathcal{C}_j$ location, as $\sigma_j$ is assumed constant over the whole surface of cell $\mathcal{C}_j$.Generated inPrediction
jd7h/texify:485f0de1ModelIDypejtbtb6t67yvub5vbj4tdvemStatusSucceededSourceWebHardwareA40Total durationCreatedPrediction
jd7h/texify:485f0de1ModelIDm4xxqp3bhtmns4ddf37ga73b2eStatusSucceededSourceWebHardwareA40Total durationCreatedPrediction
jd7h/texify:485f0de1ModelIDtiepj5tbmha5pbrwos4lcedauuStatusSucceededSourceWebHardwareA40Total durationCreatedInput
- image
- katex_compatible
Output
Then the results are that afterward: For every value of $\lambda$, there is a probability of $|\langle\Psi|\Psi_\lambda\rangle|^2$ that the system is in state $|\Psi_\lambda\rangle$ This is captured by the density matrix formalism as the transition $|\Psi\rangle\langle\Psi|\Rightarrow\sum_\lambda|\langle\Psi|\Psi_\lambda\rangle|^2|\Psi_\lambda\rangle\langle\Psi_\lambda|$ atyy I guess thinking about it classically, Demystifier's argument must be right.Generated in
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