経路積分問題

Problem 7-10For any quadratic functional, if we write\begin{equation}x(t)=\bar{x}(t)\langle 1 \rangle,\quad \langle x(t)...

Problem 7-9Use this result Eq. (7-68) to show that if \(S\) corresponds to a harmonic oscillator\begin{equation}S=\frac{...

Problem 7-8Find the transition element \(\langle x(t)x(s)\rangle =f(t, s)\) when the potential is not constant but, rath...

Problem 7-7Show that for any quadratic action\begin{equation}\langle x(t) \rangle = \bar{x}(t)\langle 1 \rangle\tag{7-57...

Problem 7-6Show, for a particle moving in three-dimentional space \(x,y,z,\)\begin{equation}\Big\langle \big(x_{k+1}-x_k...

Problem 7-5The result in another way is\begin{equation}\def\ppdiff#1#2{\frac{\partial #1}{\partial #2}}\left\langle\frac...

Problem 7-4Consider the path integral\begin{equation}\def\ppdiff#1#2{\frac{\partial #1}{\partial #2}}\int \mathscr{D}x(t...

Problem 7-3Show that \(\displaystyle{\frac{\delta F}{\delta j(\mathbf{r},s)}}\), where\begin{equation}\def\mb#1{\mathbf{...

Problem 7-2If \(F=x(\tau)\), show that \begin{equation}\frac{\delta F}{\delta x(s)}=\delta(\tau-s)\tag{7-26}\end{equatio...

Problem 7-1If \(\displaystyle{S=\int_{t_1}^{t_2} L(\dot{x},x,t)\,dt}\), show that, for any \(s\) inside the range \(t_1\...

Problem 6-12Assume that \(V(\mathbf{r})\) is independent of time and show that the time integral of the second-order sca...

Problem 6-11Suppose the diatomic molecules are oriented in a random fashion. Show that the electron scattering averaged ...