Lets say we have a 1 dimensional system with coordinate $x$ and the associated operator $\hat x$ with eigenstates $|x\rangle$. A function of $x$ is defined as $$ f(x) = \langle x |f\rangle \tag{1} $$ Now we introduce a new coordinate $y$ with operator $\hat y $ and corresponding eigenstates. x an...

Consider that we are working with a joint system composed of system A with basis $|\alpha_j\rangle$ and system B with basis $|\beta_j\rangle$, we may write a general density matrix for the joint system with respect to tensor product basis $|\alpha_j\rangle |\beta_j\rangle$. I want to understand...

In a physics class, I learned about Van Der Waals forces that allow geckos to stick. Do they have any relation to the Van Der Waals Equation relating gas pressure to temperature and volume?

In microcanonical ensemble we have $N$ representative systems ($N \rightarrow \infty)$ characterized by macroscopic parameters $N,V,E$. These systems are isolated. Then we allow them to exchange energy through thermal contact and they reach equilibrium at constant temperature $T$ and we obtain a...

I have been thinking about a certain step in hafting an axe which I can't seem to explain physically. As a reference, I've found a forestry manual which explains the process, in case my explanation is not clear. Basically, after ensuring a close fit, you put the head onto the handle. Then, to fu...

I understand chaotic motion to mean that very small perturbations in the initial starting condition can lead to very different trajectories in phase space. For this reason, we can never predict the motion accurately, because we can never have 100% accurate initial conditions. Can we look at the i...