Investigating the elementary process of diffusion yielded the universal expression of diffusivity relevant to the angular momentum of each microparticle in a material. Using the diffusivity obtained then for the diffusion equation, the wave equation of Schrödinger was theoretically derived from the physical concept in Newton mechanics. The derivation itself reveals that any moving microparticle has the wave image as an intrinsic nature. It was theoretically revealed that the relation having been accepted as a hypothesis proposed by De Broglie is valid for any moving microparticle and that another relation of matter-wave is possible. The new diffusion theory based on the matter-wave will be useful for further development of the nanotechnology in materials science.Investigating the elementary process of diffusion yielded the universal expression of diffusivity relevant to the angular momentum of each microparticle in a material. Using the diffusivity obtained then for the diffusion equation, the wave equation of Schrödinger was theoretically derived from the physical concept in Newton mechanics. The derivation itself reveals that any moving microparticle has the wave image as an intrinsic nature. It was theoretically revealed that the relation having been accepted as a hypothesis proposed by De Broglie is valid for any moving microparticle and that another relation of matter-wave is possible. The new diffusion theory based on the matter-wave will be useful for further development of the nanotechnology in materials science.

International Journal of Fundamental Physical SciencesSep 1, 20193 citations

The Statistical Foundations of Entropy

John D. Ramshaw

This book presents an innovative unified approach to the statistical foundations of entropy and the fundamentals of equilibrium statistical mechanics. These intimately related subjects are often developed in a fragmented historical manner which obscures the essential simplicity of their logical structure. In contrast, this book critically reassesses and systematically reorganizes the basic concepts into a simpler sequential framework which reveals more clearly their logical relationships. The inherent indistinguishability of identical particles is emphasized, and the resulting unification of classical and quantum statistics is discussed in detail. The discussion is focused entirely on fundamental concepts, so applications are omitted. The book is written at the advanced undergraduate or beginning graduate level, and will be useful as a concise supplement to conventional books and courses in statistical mechanics, thermal physics, and thermodynamics. It is also suitable for self-study by those seeking a deeper and more detailed analysis of the fundamentals.This book presents an innovative unified approach to the statistical foundations of entropy and the fundamentals of equilibrium statistical mechanics. These intimately related subjects are often developed in a fragmented historical manner which obscures the essential simplicity of their logical structure. In contrast, this book critically reassesses and systematically reorganizes the basic concepts into a simpler sequential framework which reveals more clearly their logical relationships. The inherent indistinguishability of identical particles is emphasized, and the resulting unification of classical and quantum statistics is discussed in detail. The discussion is focused entirely on fundamental concepts, so applications are omitted. The book is written at the advanced undergraduate or beginning graduate level, and will be useful as a concise supplement to conventional books and courses in statistical mechanics, thermal physics, and thermodynamics. It is also suitable for self-study by those seeking a deeper and more detailed analysis of the fundamentals.

WORLD SCIENTIFIC eBooksOct 3, 201718 citations

The Problem of Indistinguishable Particles

Bas C. van Fraassen

Princeton University Press eBooksDec 8, 20203 citations

Bose statistics : before and after

Narasimhaiengar Mukunda

This paper gives a historical perspective to the gestation and birth of Bose-Einstein (BE).As is known today, particles whose spin is an even multiple of $\\hslash/2$ obey BE statistics, those whose spin is an odd multiple of $\\hslash/2$ obey FD statistics. (These particles may be elementary or composite.) Both statistics are derived from the fact that particles in the quantum realm are indistinguishable, the difference being that in the FD case at most one particle can occupy any given quantum state (Pauli principle) while in the BE case any number of particles can be in a particular state. Little of this was known when the statistics were first developed by Bose. The paper gives the background of attempts to explain the black-body spectrum, which led eventually to Bose's combinatorical derivation of the Planck law using the concept of indistinguishability. (Bose was professor of physics at Dacca, in what is now Bangladesh, then India.) Einstein was the first to appreciate Bose's work, translating the paper into German for publication in Zeitschrift für Physik, and applying the methods to a quantum gas (hence, "Bose-Einstein condensation", which explains the bizarre behavior of liquid ${\\rm He}^4$ ). \n\nThis paper gives a historical perspective to the gestation and birth of Bose-Einstein (BE).As is known today, particles whose spin is an even multiple of $\\hslash/2$ obey BE statistics, those whose spin is an odd multiple of $\\hslash/2$ obey FD statistics. (These particles may be elementary or composite.) Both statistics are derived from the fact that particles in the quantum realm are indistinguishable, the difference being that in the FD case at most one particle can occupy any given quantum state (Pauli principle) while in the BE case any number of particles can be in a particular state. Little of this was known when the statistics were first developed by Bose. The paper gives the background of attempts to explain the black-body spectrum, which led eventually to Bose's combinatorical derivation of the Planck law using the concept of indistinguishability. (Bose was professor of physics at Dacca, in what is now Bangladesh, then India.) Einstein was the first to appreciate Bose's work, translating the paper into German for publication in Zeitschrift für Physik, and applying the methods to a quantum gas (hence, "Bose-Einstein condensation", which explains the bizarre behavior of liquid ${\\rm He}^4$). \n\n

Jun 1, 19943 citations

Symmetry and the indistinguishability of classical particles

Domenico Costantini

Physics Letters ASep 1, 198717 citations

This paper gives a historical perspective to the gestation and birth of Bose-Einstein (BE).As is known today, particles whose spin is an even multiple of

\\hslash/2

obey BE statistics, those whose spin is an odd multiple of

\\hslash/2

obey FD statistics. (These particles may be elementary or composite.) Both statistics are derived from the fact that particles in the quantum realm are indistinguishable, the difference being that in the FD case at most one particle can occupy any given quantum state (Pauli principle) while in the BE case any number of particles can be in a particular state. Little of this was known when the statistics were first developed by Bose. The paper gives the background of attempts to explain the black-body spectrum, which led eventually to Bose's combinatorical derivation of the Planck law using the concept of indistinguishability. (Bose was professor of physics at Dacca, in what is now Bangladesh, then India.) Einstein was the first to appreciate Bose's work, translating the paper into German for publication in Zeitschrift für Physik, and applying the methods to a quantum gas (hence, "Bose-Einstein condensation", which explains the bizarre behavior of liquid

{\\rm He}^4

). \n\n