Consider any differentiable transformation $q_{j}\rightarrow q_{j}^{\lambda} = f_{j}^{\lambda}(q_{1}, \ldots, q_{N})$ parametrized by $\lambda$ (I'll place it as a superscript). For any such transformation, we can write $$ L(q_{j}^{\lambda}, \dot{q}_{j}^{\lambda}, t) - L(q_{j}^{0}, \dot{q}_{j}^{0...

Physics professors I have had (including Dr. Feynman in 1962) contend that an infinite universe would produce a fairly uniform "glow" from our point of view, which is not present. This seems to be contradicted by a few simple factors: The light from a star reaching the earth decreases as the cub...

I'm currently studying atomic physics and have encountered a topic that I find challenging. My question is regarding the collision between a photon with an energy of, let's say, 12.20 eV and an atom. During this collision, the electron in the ground state can be excited to reach either the second...