経路積分問題

経路積分問題

問題 8-3 の解答例

Problem 8-3 Show that \(Q^{c}_{\alpha}\), \(Q^{s}_{\alpha}\) are normanl coordinates, representing, however, standi...
経路積分問題

問題 8-2 の解答例

Problem 8-2 Show that the matrix \begin{equation*} \tau_{jk}=\sum_\alpha \frac{a_{j\alpha}a_{k\alpha}}{\omega_\al...
経路積分問題

問題 8-1 の解答例

Problem 8-1 Note that the amplide to go from any state \(f(x)\) to another state \(g(x)\) is the transition amplit...
経路積分問題

問題 7-17 の解答例

Problem 7-17 Prove Eq. (7-99) : \begin{equation} \def\ppdiff#1#2{\frac{\partial #1}{\partial #2}} \def\pdiff#1{\...
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}...