経路積分問題

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

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

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

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

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

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

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

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

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

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

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

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