経路積分問題

Problem 8-5 A transition element which employs the same wave function as both the initial and final states is called an ...

Problem 8-4 Show that the ground-state wave function for the lagrangian of Eq. (8-78) can be written \begin{equation} \P...

Problem 8-3 Show that \(Q^{c}_{\alpha}\), \(Q^{s}_{\alpha}\) are normanl coordinates, representing, however, standing wa...

Problem 8-2 Show that the matrix \begin{equation*} \tau_{jk}=\sum_\alpha \frac{a_{j\alpha}a_{k\alpha}}{\omega_\alpha} \e...

Problem 8-1 Note that the amplide to go from any state \(f(x)\) to another state \(g(x)\) is the transition amplitude \(...

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

Problem 7-16 Show that \begin{equation} \def\pdiff#1{\frac{\partial}{\partial #1}} \Bigg\langle \chi \Bigg| x_l m\frac{x...

Problem 7-15 Show that the rule works for two successive momenta, that is, \begin{align} \Bigg\langle \chi \Bigg| m\frac...

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

Problem 7-13 Show that \begin{equation} \def\BraKet#1#2#3{\langle #1 | #2 | #3 \rangle} \BraKet{\chi}{m\ddot{x}}{\psi} =...

Problem 7-12 Show, if \(V\) is any function of position only, that \begin{equation} \left\langle \chi \left| \frac{dV}{d...

Problem 7-11 Show that \begin{equation} \def\pdiff#1{\frac{\partial}{\partial #1}} \def\ppdiff#1#2{\frac{\partial #1}{\p...