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我们曾在 多电子原子 中讨论过类似的定性问题。现在我们用更加定量的语言描述角动量耦合。 角动量耦合角动量之和两个电子自旋的状态可以描述为角动量相加$\hat J=\hat j_1+\hat j_2$，简单验证可知其也是角动量： [\hat J_x,\hat J_y]=[\hat j_{1x}+\hat j_{2x},\hat j_{1y}+\hat j_{2y}]=i\hbar \hat J_z角动量的描述描述角动量之和有两种方式（两种基底）： $|j_1,j_2,m_1,m_2\rangle=|j_1,m_1\rangle|j_2,m_2\rangle$ 即为非耦合基底； $|j_1,j_2,J,m\rangle$ 即为耦合基底。 我们先来验证这两种表示方式的合理性（即这四个物理量是否守恒且互相对易，构成一组CSCO）： 对于非耦合基底，显然：$[\hat{j}^2_1,\hat{j}^2_2]=0,[\hat{j}^2_1,\hat{j}_{1z}]=0,[\hat{j}^2_1,\hat{j}_{2z}]=0,[\hat{j}^2_2,\hat{j}_{1z}]=0,[\h ...

Contend 托福阅读 托福听力杂谈 托福听力题型与结构 口语语料 托福口语Task1 托福口语Task1范例 托福口语Task2 托福口语Task3 托福口语Task4 托福写作 托福写作词汇计划 托福写作范文 词以类记Content 托福首考有感

参考资料 学术写作 题型 结构 Sample 1 - Comparison Sample 2 - Evaluation Sample 3 - Argument Sample 4 - Solution 综合写作 题型 材料结构 文章结构 Sample - Opposite - TPO 40 参考资料Vince9120 学术讨论 Academic Discussion Vince9120 综合写作 Integrated Writing。此部分被UP下架，但仍有完整版视频。 学术写作第一道写作题目为学术写作（Writing for an Academic Discussion），这个新任务取代了之前的独立写作任务，旨在模拟现实情况中由老师提问、由学生主导的学术讨论。实际上和独立写作没有区别。 Time：10 minutes; Words：At least 100 words, preferably 180 words. Task： Read the questions asked by the teacher; Read the response maded by the t ...

Education Develoment TPO - 55 - Field Trip TPO - 56 - History TPO - 59 - Lands 真题76 - Funds for art 真题77 - carfree zone 真题78 - job sharing EducationDevelomentTPO - 55 - Field TripI believe that field trips are essential for students since it provides unique experience to students, which can deepen their insights into the world. To be more specific, field trips give students the opportunity to have hands-on experiences tailored to them instead of repetitive routine of their school life, enr ...

逻辑连接词 逻辑连接词 逻辑关系 连词作用 介词作用 副词作用 原因 becausesinceforas because ofdue toowning toon account ofas a result ofby reason ofthanks toon the grounds ofby virtue ofgiven that 结果 so thereforetherebythushenceas a resultas a consequenceconsequentlyaccordingly 转折 butwhileyetwhereas howevernonethelessneverthelessstill 对比 whilewhereas on the contrastby contrast 并列 andbotheitherneitheras well asnot only … but also 递进 Apart frombesides moreoverfurthermorein additionadditionallybesidesal ...

本专栏的范例除了自己的答案，其他来源于《吴奇老师的托福口语秀》和KIMI AI。该题为什么被称为独立口语题？因为这是托福口语考试中唯一一道不需要你听或者读任何材料，只需要表达自己观点的题目。 题型该题有两种题型： Do you agree of disagree with the following statement?… Some people … and other people … . Which do you think better/ do you prefer? 然后都会加一句：Use details and examples to explain your opinion. 时间15s准备，45s作答。 结构1最多回答两个原因并且进行解释，否则不能具体。如果选择只说一个原因，那么： 表达观点（5-10s）：Honestly, I think … is better/ I prefer …/ I agree (with the statement) that … 说原因（5s） 给解释（20-30s） 结尾：Therefore, I agree with the ...

TPO 真题 2024年8月 2024年7月 2024年6月 2024年5月 2024年4月 2024年3月 2024年2月 2024年1月TPOTPO 1 Some people believe that television has had a positive influence on society. Others believe it has had a negative influence on society. Which do you agree with and why? Use details and examples to explain your opinion. Television has both positive and negative impacts on society, but I lean towards the positive side. Firstly, television is a powerful educational tool. For instance, educational programs like “Se ...

本篇笔记来源于小红书不爱酸苦辣。 题目 Reading: School’s Announcement; Students’ Proposal. Conversation between a man and a woman: Agree; Disagree. Speaking: The woman expresses her opinion about the proposal described in the letter. Briefly summarize the proposal, Then state her opinion about the proposal and explain the reasons she gives for holding that opinion. Brief Summary; State the Opinion; Explain Reasons.时间 Reading: 45s; Conversation: ~90s; Preparing: 30s; Speaking: 60s. Summary: ~15s; State: &l ...

本篇笔记来源于小红书不爱酸苦辣。 题目 Reading: Article of a concept including definition and explanation. Lecture: An illustration with example of the concept. Speaking: Explain the concept of overclaiming and how the professor’s example illustrates it. Concept definition; Lecture illustration; Lecture example.时间 Reading: 45s; Lecture: ~90s; Preparing: 30s; Speaking: 60s. Definition: ~15s; Illustration: ~10s; Example: ~35s. NoteReading: 重点看标题的概念信息，并且迅速定位文中的定义句； 把定位句抄下来； 适当记忆其他的解释。 Overclaiming People ge ...

本篇笔记来源于小红书不爱酸苦辣。 题目 Lecture: Usually 2 [aspects] of a topic. First [explanation1] with [example1] Second [explanation2] with [example2] The aspect is usuallly about: advantages changes ways features strategies Speaking: Using the professor’s points and examples, summarize the lecture about [aspect]. Summary; Aspect 1 with example 1; Aspect 2 with example 2;时间 Lecture: 120~150s; Preparing: 20s; Speaking: 60s. Summary: ~10s; Aspect 1: ~25s; Aspect 2: ~25s. NoteListening: 前20~30s不需要记笔 ...