I’ve seen two derivations of the catenary equation: one involving Lagrange multipliers and another using a balance of forces on a segment of the cable/rope. I’m trying to derive the catenary equation by minimizing the potential energy of the cable, which is: $$U=\mu g \int_{x_1}^{x_2}y(x) \sqrt{1...

I understand that when the electron and proton are arranged to form a hydrogen atom, the potential energy of the system is lower than when separated. As a result, according to mass-energy equivalence, the mass of the hydrogen atom is lower. However, my question is about the physical process throu...

There is no evidence to support that time is quantized. So wouldn't the use of discrete values like $dt$ in calculus suggest time is quantized and comes in discrete durations of $dt$?

By this question, a particle can tunnel to inside a potential barrier. One aspect of this process that was not addressed in the answers was the conservation of energy. Motivated by this question, I am under the impression that having a particle inside a potential barrier would make for a higher e...