経路積分問題

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

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

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

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

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

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

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

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

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

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

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

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