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Topic Review
Understand Quantum Physics
At its core, quantum physics (also known as quantum mechanics) is the set of rules that governs the universe at the smallest possible scales—the level of atoms, electrons, photons, and other subatomic particles. It's a fundamental theory in physics that provides a description of the physical properties of nature at that scale, a realm where the classical physics of Isaac Newton no longer applies. The reason it seems so strange is that things in the quantum world behave in ways that are completely counterintuitive to our everyday experience. Classical physics works perfectly for describing how a ball flies through theair or how planets orbit the sun. But when you zoom way in, those familiar rules break down, replaced by a world of probabilities and paradoxes.
  • 214
  • 05 Sep 2025
Topic Review Peer Reviewed
Derivation of the Schrödinger Equation from Fundamental Principles
Schrödinger’s path to the quantum mechanical wave equation was heuristic and guided more by physical intuition than formal deduction. Here we derive the Schrödinger equation for the particle’s wave function Ψ, assuming that the complex function Ψ(t,𝑟⃗ ) has a meaning of the probability amplitude to find the particle at time 𝑡 at point 𝑟⃗ and the relations 𝐸=ℏ𝜔, 𝑝⃗ =ℏ𝑘⃗ expressing particle energy and momentum in terms of the frequency and wave vector of the associated probability wave.
  • 192
  • 14 Apr 2026
Topic Review Peer Reviewed
Wigner Functions
Wigner functions are a distribution function on phase space that allow to represent the state of a quantum-mechanical system. They are in many ways similar to classical phase space probability distributions, but can, in contrast to these, be negative. A description of a quantum system in terms of Wigner functions is equivalent to the more widely used one in terms of density operators or wave functions, but has advantages in visualizing properties of a quantum state and in studying the quantum–classical transition.
  • 168
  • 15 Aug 2025
Topic Review Peer Reviewed
Quantum Computing: A Concise Introduction
Quantum computing is an emerging field in computing technology that harnesses the principles of quantum mechanics—including superposition, entanglement, and quantum tunneling—to process information in fundamentally new ways. While classical computers use bits that represent states of either 0 or 1, quantum computers use quantum bits, or qubits. Unlike classical bits, a qubit can exist in a superposition of the logical states 0 and 1 simultaneously. This property allows quantum-powered systems to perform certain complex computations much faster than classical computing systems. Quantum computing holds great potential to transform many sectors by enabling breakthroughs in quantum cryptography, information retrieval, optimization, and artificial intelligence. Through quantum algorithms such as Grover’s and Shor’s algorithms, quantum computers can significantly accelerate the speed of data searching and break encryption systems that would take classical computers billions of years to crack. While still in the relatively early stages of development, quantum computers hold considerable potential to shape our next generation of computing.
  • 153
  • 24 Oct 2025
Topic Review Peer Reviewed
Extra Dimensions in Quantum Newtonian Cosmology
This entry surveys the role of extra dimensions in Newtonian quantum cosmology, with particular emphasis on large, compactified, and warped dimensional geometries and their impact on the Newtonian potential in the early universe. The discussion begins with a review of Kaluza–Klein type toy models, followed by models with large extra dimensions in which gravity propagates into a higher-dimensional bulk, producing Yukawa-like modifications to the inverse-square law at submillimeter scales. Compactification schemes on toroidal and spherical dimensions are then examined, yielding the spectrum of Kaluza–Klein modes and quantifying their corrections to the Newtonian potential. Warped extra dimensions of the Randall–Sundrum type are also considered, in which a warp factor dimension is introduced; the resulting modifications to the Newtonian interaction in quantum-corrected cosmological settings are discussed in detail.
  • 29
  • 02 Apr 2026
Topic Review
The Duality Axiom: Consciousness, Collapse, and Single Reality
A new Duality Axiom is proposed to solve the quantum measurement problem by defining consciousness as the mechanism for single reality selection.
  • 24
  • 15 Dec 2025
Topic Review
General Relativity and Quantum Field Theory
General Relativity and Quantum Field Theory (GR-QFT) represents the fundamental theoretical intersection between the physics of gravitation and the mechanics of subatomic particles. While General Relativity describes the macro-scale curvature of spacetime, Quantum Field Theory provides the framework for understanding particle interactions within quantized fields. The unification of these two paradigms is a primary goal of modern physics, aiming to establish a consistent mathematical structure that operates without singularities across all scales.
  • 21
  • 13 Apr 2026
Topic Review Peer Reviewed
Grover Quantum Algorithm: Applications and Limits
The Grover algorithm is a fundamental quantum algorithm that achieves a quadratic speedup for unstructured search problems, requiring O(√N) queries instead of O(N) classically. It works by repeatedly applying an oracle and a diffusion operator to amplify the probability of marked states. This advantage makes it relevant to cryptography, optimization, and constraint satisfaction and as a general primitive via amplitude amplification in areas like quantum machine learning and simulation. However, practical implementations are severely constrained by current noisy intermediate-scale quantum (NISQ) machines with limited coherence, deep oracle circuits, and lack of scalable Quantum RAM, restricting demonstrations to small-scale experiments with reproducibility challenges.
  • 17
  • 14 Apr 2026
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