Einstein-Podolsky-Rosens paper in 1935 is discussed in parallel with an EPR experiment on $K^0bar{K}^0$ system in 1998, yielding a strong hint of distinction in both wave-function and operators between particle and antiparticle at the level of quantu
m mechanics (QM). Then it is proposed that the CPT invariance in particle physics leads naturally to a basic postulate that the (newly defined) space-time inversion (${bf x}to -{bf x},tto -t$) is equivalent to the transformation between particle and its antiparticle. The evolution of this postulate from nonrelativistic QM via relativistic QM till the quantum field theory is discussed in some detail. The Klein paradox for both Klein-Gordon equation and Dirac equation is also discussed. Keywords: CPT invariance, Antiparticle, Quantum mechanics, Quantum field theory
Based on the precision experimental data of energy-level differences in hydrogenlike atoms, especially the 1S-2S transition of hydrogen and deuterium, the necessity of establishing a reduced Dirac equation (RDE) with reduced mass as the substitution
of original electron mass is stressed. The theoretical basis of RDE lies on two symmetries, the invariance under the space-time inversion and that under the pure space inversion. Based on RDE and within the framework of quantum electrodynamics in covariant form, the Lamb shift can be evaluated (at one-loop level) as the radiative correction on a bound electron staying in an off-mass-shell state--a new approach eliminating the infrared divergence. Hence the whole calculation, though with limited accuracy, is simplified, getting rid of all divergences and free of ambiguity.
When a particle is in high speed or bound in the Coulomb potential of point nucleus, the variation of its mass can be ascribed to the variation of relative ratio of hiding antimatter to matter in the particle. At two limiting cases, the ratio approaches to 1.
Why does the $i=sqrt{-1}$ appear essentially in the quantum mechanics? Why are there operators and noncommutativity (the uncertainty relation) in the quantum mechanics? Why are these two aspects closely related and indivisible? In probing these problems, a new point of view is proposed tentatively.
What is the momentum spectrum of a particle moving in an infinite deep square well? Einstein, Pauli and Yukawa had adopted different point of view than that in usual text books. The theoretical and experimental implication of this problem is discussed.
