This paper reviews the partial contents of our two manuscripts displayed on arXiv and the nine published papers in some journals, and offers some new expressions. These contents explore the interpretation or research of some concepts and quantum phenomena in quantum mechanics, including foundational or fundamental issues, which delve into deeper questions beneath the basic principles. In our research, we primarily focus on the absence of interaction, or restore the external field potential energy to the interaction energy and consider the related environment qualitatively. We offer a slightly more accessible explanation for several typical quantum phenomena explained using counterintuitive coherent superposition states, summarizing that the wave nature of a particle, i.e., coherent superposition, originates from the interaction of a particle with the environment. We try to propose adding a new postulate to the fundamental postulates or principles of quantum mechanics, which we call the zeroth postulate: any material particle is not free, meaning that the interaction between a particle with its environment cannot be zero. This provides a possible foundation for understanding the wave nature of microscopic particles in quantum mechanics, specifically the coherent superposition pure states. To put this into practice, we propose a new double-slit experiment, hoping that someone will conduct it and predicting that the experimental results will show interference patterns while also identifying which slit a particle has passed through, thus resolving the which-way dilemma. Additionally, we provide explanations for quantum measurements and conservation laws different from those in general books of quantum mechanics.

The recent two papers have successively proposed the concepts and more precise expressions of strict conservation or statistical conservation of physical quantities, which are different from the expression of a conserved quantity in quantum mechanics. The Hamiltonian operator of the system discussed in this paper are independent of time, so it is commutative with the operators of an angular momentum itself, its component and its square, so that all these quantities are conserved quantities. In an isolated composite system, one of the angular momentum components of the total system are strictly conserved, while the angular momentum components of the subsystems can only be conserved statistically, both of which can be expressed in terms of eigenvalues and eigenfunctions. Generally, angular momentum itself does not have eigenvalues and eigenfunctions, so it cannot be expressed as strict conservation in terms of these concepts. Although there are eigenvalues and eigenfunctions for the square of angular momentum, they cannot express strict conservation either. And they can only be expressed as statistical conservation.

Bohr et al. once believed that both the conservation of energy and the conservation of momentum in a microscopic process are statistically conserved. And then Bothe et al. verified that the laws of the conservations of total energy and total momentum of an electron and an X-ray photon before and after a single collision are strictly valid by using the Compton scattering experiment, and such results also denied statistical conservation. There are expressions about strict conservations of total energy and total momentum of the system in Compton scattering experiment without quantum mechanical concepts in the introductions of some quantum mechanics books. Different from this, the aim of this paper is attempt to express those with quantum mechanical concepts. There is no expression about the strict conservation and the statistical conservation of physical quantities in quantum mechanics books. Our viewpoints are that the total energy and the total momentum of an isolated system are strict conservation by exchanging energy and momentum within the system in the evolution of the system state, and the momentum and kinetic energy (an interaction energy is not all belong to anyone subsystem) of a subsystem are statistical conservation. The “strict conservation” in journal articles is different from ours. A recent paper by the corresponding author of this paper and his coauthors (Int.J Theor. Phys. , 2020, 59 : 229) used the terms of strict conservation and statistical conservation (we offer more precise statements in this paper, and these statements have some differences with that of a conserved physical quantity) , and offered the expression ways of the strict conservation of total momentum for an isolated composite system and the statistical conservation of momentum for a subsystem in terms of the concepts of entangled states and eigenvalues. In this paper, we try to use these concepts and mixed states to express the strict conservations of total energy and total momentum of the system before and after a Compton scattering, and also explain the statistical conservations of energy (no interaction after scattering) and momentum of a subsystem. Similarly, we can express the strict conservations of some physical quantities of an isolated composite system and the statistical conservations of some physical quantities of a subsystem with quantum mechanical concepts.