経路積分問題

経路積分問題

問題 7-7 の解答例

Problem 7-7 Show that for any quadratic action \begin{equation} \langle x(t) \rangle = \bar{x}(t)\langle 1 \rangl...
経路積分問題

問題 7-6 の解答例

Problem 7-6 Show, for a particle moving in three-dimentional space \(x,y,z,\) \begin{equation} \Big\langle \big(x...
経路積分問題

問題 7-5 の解答例

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

問題 7-4 の解答例

Problem 7-4 Consider the path integral \begin{equation} \def\ppdiff#1#2{\frac{\partial #1}{\partial #2}} \int \m...
経路積分問題

問題 7-3 の解答例

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

問題 7-2 の解答例

Problem 7-2 If \(F=x(\tau)\), show that \begin{equation} \frac{\delta F}{\delta x(s)}=\delta(\tau-s) \tag{7-26}...
経路積分問題

問題 7-1 の解答例

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 ...
経路積分問題

問題 6-12 の解答例

Problem 6-12 Assume that \(V(\mathbf{r})\) is independent of time and show that the time integral of the second-ord...
経路積分問題

問題 6-11 の解答例

Problem 6-11 Suppose the diatomic molecules are oriented in a random fashion. Show that the electron scattering ave...
経路積分問題

問題 6-10 の解答例

Problem 6-10 Consider a diatomic molecule containing two atoms, \(A\) and \(B\), arranged with their centers at the...
経路積分問題

問題 6-9 の解答例

Problem 6-9 Suppose we introduce the fact that the atomic nucleus has a finite radius given by \begin{equation} \...
経路積分問題

問題 6-8 の解答例

Problem 6-8 In an atom the potential follows the Coulomb law only for very small radii. As the radius is increased ...