---
title: "Lecture Note 02"
author: "sin-iu ho"
date: "5 March 2020"
header-includes:
output:
pdf_document
---
# Lecture Note 02
###### tags: `Quantum Physics II`
###### date: `5 March 2020`
---
::: info
# <DIV style="text-align:center;">Chapter 7<br>Time-independent Perturbation Theory <br> 不含時微擾理論 <small>(abbr. t-indpd. Ptb. Theo.)</small></br> </DIV>
:::
indpd = potential $V$ is time-indpt.
1. no (energy) degenerate = Nondegenerate
2. degenerate

---
## §7.1: Nondegenerate Perturbation Theory <br>非簡併微擾理論 <small>(abbr. Non-degen. Ptb. Theo.)</small> </br>

### §7.1.1: General Formulation 一般表述
- Reference :book:
- **[Textbook 7.1](https://hackmd.io/YHcbMfR9SVixY6-HFj-u6A) (editing)**
- [Reference Note 01](https://hackmd.io/@ulynx/S1QuuM0V8)

~~~
點擊Details以展開速記內容，詳細分析請課後筆記。
老師舉了許多例子。
~~~
::: spoiler
$H = H^0 +\lambda H^1$
perform Taylor expan. in terms of $\lambda$

Remind:
When $\lambda=0$, $\hat{H}^0\psi^0_n=E^0_n\psi^0_n$
where $\psi^0_n$'s form a complete set of (infinite number of) states with $\left<\psi^0_m|\psi^0_n\right>=\delta_{mn}$.
$\hat{H}\psi_n=E_n\psi_{n}$

Now if $H = H^0 +\lambda H^1$, we can do Taylor expan. in terms of $\lambda$:
$\psi_n = \psi_n^0+\lambda\psi_n^1 + \lambda^2\psi_n^2+\cdots$
==We want to {"{find=$\psi_n^1=\d=f=、\sum_m\psi{(n)}_m\psi_n^0$
*
$\dfrac{e^2}{4\pi\epsilon_0}\approx$

1. E&M $\alpha = \dfrac{e^2}{4\pi\epsilon_0}\approx 137$
2. weak interation [精細結構常數](https://zh.wikipedia.org/zh-tw/%E7%B2%BE%E7%BB%86%E7%BB%93%E6%9E%84%E5%B8%B8%E6%95%B0)
3. $alpha_w = \dfrac{}and \dfrac{g_w^2"}{\E^2/m w){{Nathoal cyphey-}}
4. strong ineterriom $\alpha<1$

Fuck that shit

2. Non-relavistic expansion
e.g. Hydrogen atom

$\hat{H}=\dfrac{\hat{p}^2}{2\mu}-\dfrac{\alpha}{r}$
$\mu$ is the reduced-mass

$\dfrac{p^2}{Am}=\dfrac{\alpha}{r}$

3. heavy-quark?
$m_Q\to \infty$; $\dfrac{1}{m_Q}\to 0$
$\mu_p=\dfrac{e^2}{2m}gS$
proton spin up to spin down
proton to charmed proton
$b\bar{u} \leftrightarrow c\bar{u}$
related by symmetry
$q\bar{q}$ meson
:::

### §7.1.2: First-Order Theory 一階理論
- Reference :book:
- **[Textbook 7.1]() (editing)**
- Wikipedia：[Perturbation theory (quantum mechanics)#First order corrections](https://en.wikipedia.org/wiki/Perturbation_theory_(quantum_mechanics)#First_order_corrections)