Related papers: Introduction to the "second quantization" formalism for non-relativistic quantum mechanics: A possible substitution for Sections 6.7 and 6.8 of Feynman's "Statistical Mechanics"

Introduction to the "second quantization" formalism for non-relativistic quantum mechanics: A possible substitution for Sections 6.7 and 6.8 of Feynman's "Statistical Mechanics"

URL: http://arxiv.org/abs/1812.10732v5
Date: Mon, 16 Oct 2023 13:55:42 GMT
Title: Introduction to the "second quantization" formalism for non-relativistic quantum mechanics: A possible substitution for Sections 6.7 and 6.8 of Feynman's "Statistical Mechanics"
Abstract summary: We define the creation and annihilation operators, discuss their properties, and introduce corresponding representations of states and operators of many-particle systems. As the title of the note suggests, we cover most topics treated in sections 6.7 and 6.8 of Feynman's "Statistical Mechanics: A Set of Lectures"
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: This is a self-contained and hopefully readable account on the method of creation and annihilation operators (also known as the Fock space representation or the "second quantization" formalism) for non-relativistic quantum mechanics of many particles. Assuming knowledge only on conventional quantum mechanics in the wave function formalism, we define the creation and annihilation operators, discuss their properties, and introduce corresponding representations of states and operators of many-particle systems. As the title of the note suggests, we cover most topics treated in sections 6.7 and 6.8 of Feynman's "Statistical Mechanics: A Set of Lectures". As a preliminary, we also carefully discuss the symmetry of wave functions describing indistinguishable particles. We note that all the contents of the present note are completely standard, and the definitions and the derivations presented here have been known to many. Although the style of the present note may be slightly more mathematical than standard physics literatures, we do not try to achieve full mathematical rigor.(Note to experts: In particular we here DERIVE the (anti)commutation relations of the creation and annihilation operators, rather than simply declaring them. In this sense our approach is quite close to that of Feynman's. But we here focus on the action of creation/annihilation operators on general $N$ body wave functions, while Feynman makes a heavy use of Slater-determinant-type states from the beginning. We hope that our presentation provides a better perspective on the formalism.)

Related papers

Relativistic quantum mechanics and quantum field theory [0.0]
relativistic quantum physics differs fundamentally from the non-relativistic wave mechanics.<n>It requires a formalism allowing creation and destruction of particles.<n>This article is a semi-historic account of the intriguing new features which emerge as a part of quantum field theory.
arXiv Detail & Related papers (2025-07-10T13:54:37Z)
A pseudo-random and non-point Nelson-style process [49.1574468325115]
We take up the idea of Nelson's processes, the aim of which was to deduce Schr"odinger's equation. We consider deterministic processes which are pseudo-random but which have the same characteristics as Nelson's processes.
arXiv Detail & Related papers (2025-04-29T16:18:51Z)
Dirac-von Neumann Type Axiomatic Structure for Classical Electromagnetism [0.0]
We show the existence of a complex Hilbert Space with Hermitian operators for calculations in textitclassical electromagnetism.<n>We also demonstrate the existence of the wave commutation relationship $[hatx,hatk]=i$, which is a unique classical analogue to the canonical commutator $[hatx,hatp]=ihbar$.
arXiv Detail & Related papers (2024-12-31T20:52:35Z)
Heading towards an Algebraic Heisenberg Cut [0.0]
We show that early signs of macroscopic behaviour appear before infinity. This lays the grounds for justifying the inclusion in quantum physics of the ITP formalism.
arXiv Detail & Related papers (2024-12-21T10:39:40Z)
Interpretation of wave function by coherent ensembles of trajectories [0.0]
We revise the ensemble interpretation of wave function in quantum mechanics. We introduce coherence (auto-concordance) of ensembles of quantum trajectories in the space-time.
arXiv Detail & Related papers (2024-07-12T14:10:04Z)
Should we trade off higher-level mathematics for abstraction to improve student understanding of quantum mechanics? [0.0]
In work at Georgetown University and with edX, we have been teaching a class focused on an operator-forward viewpoint. It teaches quantum mechanics in a representation-independent fashion and allows for most of the math to be algebraic. It also allows for more advanced concepts relevant for quantum sensing, such as squeezed states, to be introduced in a simpler format than is conventionally done.
arXiv Detail & Related papers (2023-04-28T19:30:19Z)
Revisiting Quantum Contextuality in an Algebraic Framework [0.0]
We discuss the ideas of extracontextuality and extravalence, that allow one to relate Kochen-Specker's and Gleason's theorems. Our extracontextual approach requires however a way to describe the Heisenberg cut''
arXiv Detail & Related papers (2023-04-16T12:06:44Z)
Schr\"odinger cat states of a 16-microgram mechanical oscillator [54.35850218188371]
The superposition principle is one of the most fundamental principles of quantum mechanics. Here we demonstrate the preparation of a mechanical resonator with an effective mass of 16.2 micrograms in Schr"odinger cat states of motion. We show control over the size and phase of the superposition and investigate the decoherence dynamics of these states.
arXiv Detail & Related papers (2022-11-01T13:29:44Z)
A Transfer Operator Approach to Relativistic Quantum Wavefunction [0.0]
Original intent of Koopman-von Neumann formalism was to put classical and quantum mechanics on same footing. We show what transfer operators can say about quantum mechanical evolution.
arXiv Detail & Related papers (2022-10-24T00:18:02Z)
Contextual unification of classical and quantum physics [0.0]
We develop the idea that the usual formalism of quantum mechanics stops working when countable infinities of particles are encountered. This is because the dimension of the corresponding Hilbert space becomes uncountably infinite, leading to the loss of unitary equivalence. We show that it provides a natural way to describe the "Heisenberg cut", as well as a unified mathematical model including both quantum and classical physics.
arXiv Detail & Related papers (2022-09-03T16:51:19Z)
Correspondence Between the Energy Equipartition Theorem in Classical Mechanics and its Phase-Space Formulation in Quantum Mechanics [62.997667081978825]
In quantum mechanics, the energy per degree of freedom is not equally distributed. We show that in the high-temperature regime, the classical result is recovered.
arXiv Detail & Related papers (2022-05-24T20:51:03Z)
Why we should interpret density matrices as moment matrices: the case of (in)distinguishable particles and the emergence of classical reality [69.62715388742298]
We introduce a formulation of quantum theory (QT) as a general probabilistic theory but expressed via quasi-expectation operators (QEOs) We will show that QT for both distinguishable and indistinguishable particles can be formulated in this way. We will show that finitely exchangeable probabilities for a classical dice are as weird as QT.
arXiv Detail & Related papers (2022-03-08T14:47:39Z)
The Time-Evolution of States in Quantum Mechanics [77.34726150561087]
It is argued that the Schr"odinger equation does not yield a correct description of the quantum-mechanical time evolution of states of isolated (open) systems featuring events. A precise general law for the time evolution of states replacing the Schr"odinger equation is formulated within the so-called ETH-Approach to Quantum Mechanics.
arXiv Detail & Related papers (2021-01-04T16:09:10Z)
Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
arXiv Detail & Related papers (2020-06-03T17:54:43Z)
External and internal wave functions: de Broglie's double-solution theory? [77.34726150561087]
We propose an interpretative framework for quantum mechanics corresponding to the specifications of Louis de Broglie's double-solution theory. The principle is to decompose the evolution of a quantum system into two wave functions. For Schr"odinger, the particles are extended and the square of the module of the (internal) wave function of an electron corresponds to the density of its charge in space.
arXiv Detail & Related papers (2020-01-13T13:41:24Z)

This list is automatically generated from the titles and abstracts of the papers in this site.