経路積分問題

経路積分問題

問題 7-16 の解答例

Problem 7-16 Show that \begin{equation} \def\pdiff#1{\frac{\partial}{\partial #1}} \Bigg\langle \chi \Bigg| x_l ...
経路積分問題

問題 7-15 の解答例

Problem 7-15 Show that the rule works for two successive momenta, that is, \begin{align} \Bigg\langle \chi \Bigg|...
経路積分問題

問題 7-14 の解答例

Problem 7-14 Show that the transition element of \(\displaystyle{m\left(\frac{x_{k+1}-x_{k}}{\varepsilon}\right)f(x...
経路積分問題

問題 7-13 の解答例

Problem 7-13 Show that \begin{equation} \def\BraKet#1#2#3{\langle #1 | #2 | #3 \rangle} \BraKet{\chi}{m\ddot{x}}...
経路積分問題

問題 7-12 の解答例

Problem 7-12 Show, if \(V\) is any function of position only, that \begin{equation} \left\langle \chi \left| \fra...
経路積分問題

問題 7-11 の解答例

Problem 7-11 Show that \begin{equation} \def\pdiff#1{\frac{\partial}{\partial #1}} \def\ppdiff#1#2{\frac{\partia...
経路積分問題

問題 7-10 の解答例

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

問題 7-9 の解答例

Problem 7-9 Use this result Eq. (7-68) to show that if \(S\) corresponds to a harmonic oscillator \begin{equation}...
経路積分問題

問題 7-8 の解答例

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