Mathematical Principles of Theoretical Physics

5.5. STRUCTURE OF MEDIATOR CLOUDS AROUND SUBATOMIC PARTICLES 327 Consequently, if the naked hadron is white, then the gluon clou ...

328 CHAPTER 5. ELEMENTARY PARTICLES ...

Chapter 6 Quantum Physics 6.1 Introduction Quantum physics is the study of the behavior of matter and energy at molecular, atomi ...

330 CHAPTER 6. QUANTUM PHYSICS 2) gGaμrepresent the interaction potentials between the particles. 3) for an N-particle system, o ...

6.1. INTRODUCTION 331 Alsoνparticipates only the weak interaction similar to the neutrinos, and consequently pos- sesses similar ...

332 CHAPTER 6. QUANTUM PHYSICS In the Planck classical quantum assumption that the energy is discrete for a fixed frequency, and ...

6.2 Foundations of Quantum Physics. E are given by (6.2.2) position operator: xˆψ=xψ, momentum operator: pˆψ=−ih ̄∇ψ, energy ope ...

334 CHAPTER 6. QUANTUM PHYSICS In addition to these Hermitians in (6.2.2) and (6.2.5), the following 5 types of particle current ...

6.2. FOUNDATIONS OF QUANTUM PHYSICS 335 6.2.2 Quantum dynamic equations In quantum mechanics, the following are the four basic d ...

336 CHAPTER 6. QUANTUM PHYSICS wherep 0 is a scalar momentum. It follows that (6.2.12) E=cp 0 , By (6.2.5), corresponding top 0 ...

6.2. FOUNDATIONS OF QUANTUM PHYSICS 337 In fact, under the reflection transformation (6.2.17), the Dirac spinorψtransforms as (6 ...

338 CHAPTER 6. QUANTUM PHYSICS Remark 6.9.Historically the four basic quantum dynamic equations werediscovered all based on Post ...

6.2. FOUNDATIONS OF QUANTUM PHYSICS 339 Here the conjugate fields are the real and imaginary parts ofψ=ψ^1 +iψ^2. By applying th ...

340 CHAPTER 6. QUANTUM PHYSICS Principle 6.10.A conserved quantum system can be described by a set of conjugate fields Ψ= (ψ 1 , ...

6.2. FOUNDATIONS OF QUANTUM PHYSICS 341 In statistics, the error to an average value is expressed by the squared deviation. Name ...

342 CHAPTER 6. QUANTUM PHYSICS 1) If a particleAconsists ofNmore fundamental particlesAi( 1 ≤i≤N), in a small ball with radiusr, ...

6.2. FOUNDATIONS OF QUANTUM PHYSICS 343 LetHbe the Hamiltonian energy of a conservative quantum system,which can be de- scribed ...

344 CHAPTER 6. QUANTUM PHYSICS The formulas (6.2.46)-(6.2.48) are the conservation laws of the classical quantum mechanics. Henc ...

6.2. FOUNDATIONS OF QUANTUM PHYSICS 345 Notice that x 2 ∂ 2 −∂ 2 x 2 =x 3 ∂ 3 −∂ 3 x 3 =− 1. Hence we get (6.2.53) HˆLˆ 1 −Lˆ 1 ...

346 CHAPTER 6. QUANTUM PHYSICS For the Klein-Gordon fields(Ψ,Φ)T, the Hamiltonian for a central force field is given by (6.2.59) ...