One of the most used schemes for solving ordinary differential equations numerically is the fourth-order Runge-Kutta method. Why isn't it used to integrate the equation of motion of particles in molecular dynamics?

I am trying to understand the matrices and vectors presented in this section https://en.wikipedia.org/wiki/Spin_(physics)#Spin_projection_quantum_number_and_multiplicity I am looking for a reference where these objects are defined in a sufficiently precise manner that I can derive the matrices an...

Let's say we have a metal conducting wire with delocalized electrons and positive metal ions. We apply a potential difference across it. Now, the electrons will start flowing in one direction due to the electric field. If we observe from the reference frame of one of the moving electrons, won't t...

The differential equation for forced oscillation is: $$m \ddot{x} + b\dot{x}+kx = F_{o}\sin(\omega''t)$$ I don't find this equation intuitively satisfying. My mind tends to think that as $F_{o}\sin(\omega''t)$ is the restoring force, it should be equal to the damping force $b\dot{x}$. However, th...