Recent content by Matthew_

To my understanding, the most general formulation of the TDVP relies on the effective Action $$\begin{equation}\mathcal{S}=\int_{t_1}^{t_2}dt\:\mathcal{L}', \hspace{15pt} \mathcal{L}'=...

The first formulation gives the total number of electrons, the reasoning behind that sum is exactly what you reported. The expression ## n(\mathcal{E})=g(\mathcal{E}) f_D(\mathcal{E}) ##, with the same logic, actually represents the density of particles with energy ##\mathcal{E}##, being...

In the Jellium model, it is customary to evaluate the exchange term of the Hartree-Fock equation for plane waves ##\varphi_{\mathbf{k}_i}## as a correction to the energy of the non-interacting electron gas obtaining $$\hat{U}^{ex} \varphi_{\mathbf{k}_i}=-e^2 \left( \int \dfrac{\mathrm{d}^3k}{2...

Thank you, this was illuminating

We were introduced the lagrangian for a particle moving in an eletromagnetic field (for context, this was a brief introduction before dealing with Zeeman effect) as $$\mathcal{L}=\dfrac{m}{2}(\dot{x}^2_1+\dot{x}^2_2+\dot{x}^2_3)-q\varphi+\dfrac{q}{c}\vec{A}\cdot\dot{\vec{x}}.$$ A...