Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Princeton University Press eBooks

CHAPTER 3 Particles, Waves, and the Laws that Govern Them

Mark I. Strikman, Kevork Spartalian, Milton W. Cole

Published Dec 31, 2015• 0 citations
Publisher
DOI
10.1515/9781400865437-007

Related papers

Particles, Waves, and the Laws that Govern Them

Princeton University Press eBooks•Dec 21, 2014•0 citations

Modeling the Quantum World

Moamer Hasanovic

This chapter introduces core quantum mechanics concepts, focusing on Heisenberg's uncertainty principle and Schrödinger's equation, which describe quantum particles' wave–particle duality and probabilistic nature. The uncertainty principle and Schrödinger's equation are fundamental postulates validated by experiments, with the latter governing quantum behavior. The chapter explores wave functions, superposition, and entanglement, using light polarization to contrast classical and quantum interpretations, demonstrating that single photons exhibit probabilistic outcomes when interacting with polarizers. Additionally, it discusses polarizers and polarizing beam splitters, analyzing light propagation through these components using the law of Malus and comparing classical and quantum interpretations. The chapter concludes by highlighting the implications of these findings on photon polarization and measurement, providing a foundation for understanding quantum technologies.

SPIE eBooks•Aug 31, 2026•0 citations

Section XI. Waves and Particles

Harvard University Press eBooks•Dec 31, 2011•0 citations

Wave optics

T. R. Groves

The central problem in this chapter is to solve for the wave function for a particle of charge q and rest mass m propagating in a general electromagnetic potential. It explores a few of the important implications for wave optics. The chapter begins with a review of basic quantum mechanics governing particle motion. It confines the discussion to only those topics which are relevant to the motion of a fast (unbound) charged particle in a general electromagnetic potential. The chapter seeks a dynamical equation to describe the motion of a single particle of charge q and rest mass m in the presence of a general electromagnetic potential. Physically, a close analogy exists with the wave optics of light propagation. In quantum mechanical wave optics, one starts with a surface of constant phase called a wave front. In wave optics, the aberrations are manifest as displacements in the surfaces of constant phase.

CRC Press eBooks•Dec 19, 2017•0 citations

Fundamentals of Quantum Mechanics

Muhammad Suhail Zubairy

The laws of quantum mechanics were formulated in the year 1925 through the work of Werner Heisenberg, followed by Max Born, Pascual Jordan, Paul Dirac, and Wolfgang Pauli. A separate but equivalent approach was independently developed by Erwin Schrödinger in early 1926. The laws governing quantum mechanics were highly mathematical and their aim was to explain many unresolved problems within the framework of a formal theory. The conceptual foundation emerged in the subsequent 2–3 years that indicated how radically different the new laws were from classical physics. In this chapter some of these salient features of quantum mechanics are discussed. The topics include the quantization of energy, wave–particle duality, the probabilistic nature of quantum mechanics, Heisenberg uncertainty relations, Bohr’s principle of complementarity, and quantum superposition and entanglement. This discussion should indicate how different and counterintuitive its fundamentals are from those of classical physics.

Oxford University Press eBooks•May 7, 2020•6 citations

9. Waves and Particles

Kenneth W. Ford

Harvard University Press eBooks•Dec 31, 2005•0 citations
This chapter introduces core quantum mechanics concepts, focusing on Heisenberg's uncertainty principle and Schrödinger's equation, which describe quantum particles' wave–particle duality and probabilistic nature. The uncertainty principle and Schrödinger's equation are fundamental postulates validated by experiments, with the latter governing quantum behavior. The chapter explores wave functions, superposition, and entanglement, using light polarization to contrast classical and quantum interpretations, demonstrating that single photons exhibit probabilistic outcomes when interacting with polarizers. Additionally, it discusses polarizers and polarizing beam splitters, analyzing light propagation through these components using the law of Malus and comparing classical and quantum interpretations. The chapter concludes by highlighting the implications of these findings on photon polarization and measurement, providing a foundation for understanding quantum technologies.
The central problem in this chapter is to solve for the wave function for a particle of charge q and rest mass m propagating in a general electromagnetic potential. It explores a few of the important implications for wave optics. The chapter begins with a review of basic quantum mechanics governing particle motion. It confines the discussion to only those topics which are relevant to the motion of a fast (unbound) charged particle in a general electromagnetic potential. The chapter seeks a dynamical equation to describe the motion of a single particle of charge q and rest mass m in the presence of a general electromagnetic potential. Physically, a close analogy exists with the wave optics of light propagation. In quantum mechanical wave optics, one starts with a surface of constant phase called a wave front. In wave optics, the aberrations are manifest as displacements in the surfaces of constant phase.
The laws of quantum mechanics were formulated in the year 1925 through the work of Werner Heisenberg, followed by Max Born, Pascual Jordan, Paul Dirac, and Wolfgang Pauli. A separate but equivalent approach was independently developed by Erwin Schrödinger in early 1926. The laws governing quantum mechanics were highly mathematical and their aim was to explain many unresolved problems within the framework of a formal theory. The conceptual foundation emerged in the subsequent 2–3 years that indicated how radically different the new laws were from classical physics. In this chapter some of these salient features of quantum mechanics are discussed. The topics include the quantization of energy, wave–particle duality, the probabilistic nature of quantum mechanics, Heisenberg uncertainty relations, Bohr’s principle of complementarity, and quantum superposition and entanglement. This discussion should indicate how different and counterintuitive its fundamentals are from those of classical physics.