Flashcards
Quantum Mechanics II
Cards in this deck (10)
- 1Parity Relations (position, linear momentum, angular momentum, spin, total angular momentum)\[\{\pi,x\}=0\]
\[\{\pi,p\}=0\]
\[[\pi,L]=0\]
\[[\pi,S]=0\]
\[[\pi,J]=0\] - 2Wave Function under Parity\[\psi_{\pi\alpha}(x)=\psi_{\alpha}(-x)\]
- 3Parity Acting on Spherical Harmonics\[\pi=(-1)^lR_{\alpha}(r)Y_l^m\]
- 4Time Reversal Relations (position, linear momentum, angular momentum, spin, total angular momentum)\[\Theta x\Theta^{-1}=+x\]
\[\Theta p\Theta^{-1}=-p\]
\[\Theta L\Theta^{-1}=-L\]
\[\Theta S\Theta^{-1}=-S\]
\[\Theta J\Theta^{-1}=-J\] - 5First Order Energy Shift in Time-Independent Non-Degenerate Perturbation Theory\[\Delta_n^{(1)}=\]
- 6First Order Perturbed Eigenstate in Time-Independent Non-Degenerate Perturbation Theory\[|n_1>=\sum_{k_0\neq n_0}\frac{}{E_n^{(0)}-E_k^{(0)}}|k_0>\]
- 7Second Order Energy Shift in Time-Independent Non-Degenerate Perturbation Theory\[\Delta_n^{(2)}=\sum_{k_0\neq n_0}\frac{||^2}{E_n^{(0)}-E_k^{(0)}}\]
- 8The Probability of Finding the Perturbed State in the Original Eigenstatein Time-Independent Perturbation Theory\[P=|_N|^2=1-\lambda^2\sum_{k_0\neq n_0}\frac{||^2}{(E_n^{(0)}-E_k^{(0)})^2}\]
- 9Equation Used to Estimate the Ground State Energy Using Variational Method\[\tilde{H}\equiv\frac{<\tilde{0}|H|\tilde{0}>}{<\tilde{0}|\tilde{0}>}\geq E_0\]
- 10The Probability of Finding the Perturbed State in the Original Eigenstate in Time-Dependent Perturbation Theory\[P_t(i\to n)=|c_n(t)|^2=|c_n^{(1)}(t)+c_n^{(2)}(t)+\cdots|^2\]
\[c_n^{(0)}=\delta_{ni}\]
\[c_n^{(1)}(t)=\Big(\frac{-i}{\hbar}\Big)\int_0^tdt'e^{i\omega_{ni}t'}V_{ni}(t')\]