$\newcommand{\ket}[1]{\left \lvert #1 \right \rangle}$ $\newcommand{\bra}[1]{\left \langle #1 \right \rvert}$ $\newcommand{\braket}[2]{\left \langle #1 | #2 \right \rangle}$ $\newcommand{\bbraket}[3]{\left \langle #1 | #2 | #3 \right \rangle}$ Summary How do we show, from first principles, that...

Your final expression factorizes quite nicely as \begin{align} \braket{f}{\Psi'(t)} = & - \left( \frac{V_0}{\hbar} \right)^2 \sum_n \bbraket{f}{\mathcal{O}}{n} \bbraket{n}{\mathcal{O}}{i} \\ & \qquad \times \int_0^t \mathrm dt' v(t') \exp\left(i(\omega_f-\omega_n)t'\right) \\ & \qquad \quad \...

This is an attempt to gather together the various questions about time that have been asked on this site and provide a single set of hopefully authoritative answers. Specifically we attempt to address issues such as: What do physicists mean by time? How does time flow? Why is there an arrow of ...

From an aerodynamic point of view, could a full-size aircraft of X-Wing design fly in Earth's atmosphere? Assuming you were free to add control surfaces here and there, could the wings in open configuration create lift ?

Traditionally for a free electron, we presume the expectation of its location (place of the center of mass) and the center of charge at the same place. Although this seemed to be reasonable for a classical approximation (see: Why isn't there a centre of charge? Lagerbaer), I wasn't sure if it's...