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

CRC Press eBooks

Quantum Mechanics

Eduardo R. Mucciolo

Published Aug 6, 2025• 0 citations
Publisher

Abstract

Now that we went through the math and the notation, we can introduce the fundamentals of quantum mechanics in a formal and precise way.
DOI
10.1201/9781003485124-4

Related papers

A Brief Survey of Main Interpretations of Quantum Mechanics

Jarosław Pykacz

SpringerBriefs in physics•Jan 1, 2015•7 citations

Fundamentals of quantum mechanics in Liouville space

Jerryman A. Gyamfi

Abstract The purpose of this paper is to articulate a coherent and easy-to-understand way of doing quantum mechanics in any finite-dimensional Liouville space, based on the use of a Kronecker product and what we have termed the ‘bra-flipper’ operator. One of the greater strengths of the formalism expatiated on here is the striking similarities it bears with Dirac’s bra-ket notation. For the purpose of illustrating how the formalism can be effectively employed, we use it to solve a quantum optical master equation for a two-level quantum system and find its Kraus operator sum representation. The paper is addressed to students and researchers with some basic knowledge of linear algebra who want to acquire a deeper understanding of the Liouville space formalism. The concepts are conveyed so as to make the application of the formalism to more complex problems in quantum physics straightforward and unencumbered.

arXiv:2003.11472•European Journal of Physics•Jul 8, 2020•77 citations

Foundational Unknowns of Quantum Mechanics

F. J. Duarte

The unknowns that remain in quantum mechanics are not the mysteries that people often think of. The real mysteries of quantum mechanics are annexed to foundational knowledge of quantum physics that, given all indications, just appeared into existence at our measurement level, or second layer of quantum physics. These miracles of knowledge include Planck's energy equation https://www.w3.org/1998/Math/MathML" display="inline"> E = h ν , Born's rule https://www.w3.org/1998/Math/MathML" display="inline"> | ψ 〉 | ψ 〉 ∗ = | | ψ 〉 | 2 , elements of the Schrödinger equation, and Dirac's notation. In Quantum Clear we elucidate the physics leading to https://www.w3.org/1998/Math/MathML" display="inline"> E = h ν and https://www.w3.org/1998/Math/MathML" display="inline"> | ψ 〉 | ψ 〉 ∗ = | | ψ 〉 | 2 , but that's it. And it remains certain that those who introduced this wonderful knowledge did not elaborate further except for the explanation of Schrödinger who linked mathematical discovery to ‘like a great gift…’. Ward, on the other hand, described the arrival of knowledge with ‘ no way I can trace the source. ’

CRC Press eBooks•Apr 10, 2026•0 citations

Introduction to Quantum Mechanics 1

Ibrahima Sakho

Wiley eBooks•Oct 11, 2019•86 citations

ALGEBRAIC WAY OF SIMULTANEOUSLY ANALYZING BOTH EINSTEIN, PODOLSKY AND ROSEN PAPER AND BOHR'S REPLY TO IT

Nakka Gurappa

In their celebrated paper titled Can quantum mechanical description of physical reality be considered complete?, Einstein, Podolsky and Rosen (EPR) showed for the first time the existence of `Spooky action-at-a-distance'. Though the result of their paper is unquestionable, but the conclusion of the same became sensational because of its challenge to quantum mechanical formalism whether it's complete or not in describing the physical reality of Nature. Bohr's physical and philosophical reply to that conclusion justified the completeness of quantum mechanics. Here, a simple algebraic way is presented for the results of these two classic papers in such a way that the actual reason behind why quantum world necessarily exhibits the action-at-a-distance and how Bohr defended against the incompleteness of the quantum formalism will become clear.This approach naturally reveals what physical assumption of EPR went wrong while considering the entangled quantum system and also provides the missing mathematical argument in Bohr's reply.

•Jan 1, 2018•0 citations

Quantum Mechanics: Introduction to Mathematical Formulation

Martin Pieper

•May 18, 2021•0 citations
Abstract The purpose of this paper is to articulate a coherent and easy-to-understand way of doing quantum mechanics in any finite-dimensional Liouville space, based on the use of a Kronecker product and what we have termed the ‘bra-flipper’ operator. One of the greater strengths of the formalism expatiated on here is the striking similarities it bears with Dirac’s bra-ket notation. For the purpose of illustrating how the formalism can be effectively employed, we use it to solve a quantum optical master equation for a two-level quantum system and find its Kraus operator sum representation. The paper is addressed to students and researchers with some basic knowledge of linear algebra who want to acquire a deeper understanding of the Liouville space formalism. The concepts are conveyed so as to make the application of the formalism to more complex problems in quantum physics straightforward and unencumbered.
The unknowns that remain in quantum mechanics are not the mysteries that people often think of. The real mysteries of quantum mechanics are annexed to foundational knowledge of quantum physics that, given all indications, just appeared into existence at our measurement level, or second layer of quantum physics. These miracles of knowledge include Planck's energy equation https://www.w3.org/1998/Math/MathML" display="inline"> E = h ν , Born's rule https://www.w3.org/1998/Math/MathML" display="inline"> | ψ 〉 | ψ 〉 ∗ = | | ψ 〉 | 2 , elements of the Schrödinger equation, and Dirac's notation. In Quantum Clear we elucidate the physics leading to https://www.w3.org/1998/Math/MathML" display="inline"> E = h ν and https://www.w3.org/1998/Math/MathML" display="inline"> | ψ 〉 | ψ 〉 ∗ = | | ψ 〉 | 2 , but that's it. And it remains certain that those who introduced this wonderful knowledge did not elaborate further except for the explanation of Schrödinger who linked mathematical discovery to ‘like a great gift…’. Ward, on the other hand, described the arrival of knowledge with ‘ no way I can trace the source. ’
In their celebrated paper titled Can quantum mechanical description of physical reality be considered complete?, Einstein, Podolsky and Rosen (EPR) showed for the first time the existence of `Spooky action-at-a-distance'. Though the result of their paper is unquestionable, but the conclusion of the same became sensational because of its challenge to quantum mechanical formalism whether it's complete or not in describing the physical reality of Nature. Bohr's physical and philosophical reply to that conclusion justified the completeness of quantum mechanics. Here, a simple algebraic way is presented for the results of these two classic papers in such a way that the actual reason behind why quantum world necessarily exhibits the action-at-a-distance and how Bohr defended against the incompleteness of the quantum formalism will become clear.This approach naturally reveals what physical assumption of EPR went wrong while considering the entangled quantum system and also provides the missing mathematical argument in Bohr's reply.