Chapter 17 Time-Independence Perturbation Theory

Chapter 16 Variational and WKB Methods

16.1 T

Chapter 15 Addition of Angular Momenta

15.1 A

Chapter 14 Spin

14.1 Introduction

14.2 What is the Nature of Spin?

14.3 Kinematics of Spin

Exercise 14.3.1 Let us verify the above corollary explicitly. Take some spinor with components $\alpha=\rho_1 \mathrm{e}^{\mathrm{i} \phi_1}$ and $\beta=\rho_2 \mathrm{e}^{\mathrm{i} \phi_2}$. From $\langle\chi \mid \chi\rangle=1$, deduce that we can write $\rho_1=\cos (\theta / 2)$ and $\rho_2=\sin (\theta / 2)$ for some $\theta$. Next pull out a common phase factor so that the spinor takes the form in Eq. (14.3.28a). This verifies the corollary and also fixes $\hat{n}$.

Chapter 13 The Hydrogen Atom

13.1 The Eigenvalue Problem

Exercise 13.1.1 Derive Eqs. (13.1.11) and (13.1.14) starting from Eqs. (13.1.8)-(13.1.10).