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Light-front holography and the light-front coupled
Light-front holography and the light-front coupled

... standard approach is to expand the eigenstate in a truncated Fock basis, with the wave functions as the expansion coefficients, and solve the resulting integral equations for these wave functions. The light-front coupled-cluster (LFCC) method [1] follows this path, except that the Fock basis is not ...
The fractional quantum Hall effect I
The fractional quantum Hall effect I

... has to be an integer multiple of e2 /h. How can we reconcile this with the fractionally quantized plateau at ⌫ = 1/3 in Fig. 7.1? The key issue was the assumption of a unique ground state on the torus with a finite gap to the first excited state. We are now proving that this is not the case of a sta ...
The variational principle and simple properties of the ground
The variational principle and simple properties of the ground

... potentials can give rise to spontaneous symmetry breaking, as pointed out in Ref. 4. Spontaneous symmetry breaking could lead to degeneracy in the ground-state wave function and the proof given here does not hold. If the Hamiltonian is rotationally invariant, the potential depends only on r and thus ...
Quantum Mechanics I, Sheet 1, Spring 2015
Quantum Mechanics I, Sheet 1, Spring 2015

... In some physical contexts, the following operator may arise Q̂ ≡ i ...
A. Is the wave function a description of the physical world?
A. Is the wave function a description of the physical world?

... One might hold that the human failure to achieve established metaphysical results is due to some special quirk of the human mind, a quirk that could be absent from the minds of Martians or intelligent dolphins. Evolutionary biology suggests that human beings possess a very specific set of mental ta ...
Lecture 3 Operator methods in quantum mechanics
Lecture 3 Operator methods in quantum mechanics

... the momentum operator, p̂ = −i!∂x , with eigenvalue p. For every observable A, there is an operator  which acts upon the wavefunction so that, if a system is in a state described by |ψ", the expectation value of A is #A" = #ψ|Â|ψ" = ...
Multiparticle Quantum: Exchange
Multiparticle Quantum: Exchange

Wave Packets - Centro de Física Teórica
Wave Packets - Centro de Física Teórica

... Imagine an experiment where at instant t = 0 we measure the position of a quantum particle. The experiment is 100 times repeated. The time starts counting everytime at the beginning of the experiment. One obtains the following result. The particle is never found for x < −4.5, or for x > 5.5, 3 times ...
PowerPoint file of HBM_part 2
PowerPoint file of HBM_part 2

... that describes the temporary (singular) curvature of the embedding continuum. These pitches quickly combine in a ditch that like the micro-path folds along the oscillation path. These ditches form special kinds of geodesics that we call “Geoditches”. The geoditches explain the binding effect of enta ...
The Interaction of Radiation and Matter: Quantum
The Interaction of Radiation and Matter: Quantum

... defines or generates a two-dimensional Taylor expansion when it acts on a function of and . In particular, if we take the "phase space" representation of the ground or vacuum state as the product of two Gaussians (see Equations [ I-10a ] and [ I-29 ]), then representation -- i.e. ...
Many-Electron States - cond
Many-Electron States - cond

... implies that the symmetric and antisymmetric components of the many-body wave function are not mixed by the Hamiltonian: if the initial wave function is symmetric/antisymmetric, this does not change under time evolution. There is an intriguing connection between the spin of the indistinguishable par ...
Distinguishable- and Indistinguishable
Distinguishable- and Indistinguishable

and : formal 1D calculations - Sociedade Brasileira de Física
and : formal 1D calculations - Sociedade Brasileira de Física

... of the Ehrenfest equations (which does not use overly stringent assumptions), see Ref. [7]. For a more general (and rigorous) derivation, see Ref. [8]. For a nice treatment of this theorem (specifically, for the problem of a particle-in-a-box) that is based on the use of the classical force operator ...
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Chapter 1. Fundamental Theory
Chapter 1. Fundamental Theory

... Classically: ψ(r,t) = δ(r − vt) , i.e., the exact location and velocity at any given time t is known. Quantum Mechanically: Δpx ⋅ Δx ≥  (Heisenberg’s Uncertainty Principle). Connection: (1) when  → 0 , quantum mechanics (QM) reduces to classical mechanics. (2) Correspondence principle: QM must app ...
Lecture 2: Bogoliubov theory of a dilute Bose gas Abstract
Lecture 2: Bogoliubov theory of a dilute Bose gas Abstract

... by wave functions for N identical particles that are symmetric under any permutation of the particles labels. This “big” many-particle Hilbert space is called the boson Fock space in physics. The rule to change the representation of operators from the Schrödinger picture to the second quantized lan ...
Zero field Quantum Hall Effect in QED3
Zero field Quantum Hall Effect in QED3

introduction to the many-body problem
introduction to the many-body problem

... The Fock space is spanned by the states |n1 , n2 , . . . , ni , . . .i. Therefore an arbitrary state can be obtained by acting on |0i by some polynomial of creation operators a†i . To illustrate the formalism, we consider a few simple examples. (1) As a first example we consider an atom where the si ...
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... a) Fundamental behaviors of the wave function A wave function must be Single valued: A single-valued function is function that, for each point in the domain, has a unique value in the range. Continuous: The function has finite value at any point in the given space. Differentiable: Derivative of wave ...
3.1 Fock spaces
3.1 Fock spaces

Variational principle in the conservation operators deduction
Variational principle in the conservation operators deduction

...  E ()    [ ( x, y, z ) H ( x, y, z )] dxdydz  0 where E ( ) means the total energy functional depended on the psi-function  ; ...
4.Operator representations and double phase space
4.Operator representations and double phase space

... This is most appropriate for quantum chaos, because it highlights the classical region. But this coarse-graining of the quantum interferences is not an advantage for quantum information theory: The opposite of the chord function. ...
Uncertainty Relations for Quantum Mechanical Observables
Uncertainty Relations for Quantum Mechanical Observables

... more: Let ψ, ξ be two states (representing particles). We first want to measure A on ψ. We assume that every meaurement includes interaction with another particle (cf. measurement of car speed with radar gun). So for the A-measurement, ψ interacts with ξ. Then a third observable M of ξ is supposed t ...
Snímek 1 - Fordham University Computer and Information Sciences
Snímek 1 - Fordham University Computer and Information Sciences

Quantum Field Theory I
Quantum Field Theory I

... Quantum Field Theory is sometimes called “2nd quantization.” This is a very bad misnomer because of the reason I will explain later. But nonetheless, you are likely to come across this name, and you need to know it. The aim of the quantum field theory is to come up with a formalism which is complete ...
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Second quantization

Second quantization is a formalism used to describe and analyze quantum many-body systems. It is also known as canonical quantization in quantum field theory, in which the fields (typically as the wave functions of matters) are thought of as field operators, in a similar manner to how the physical quantities (position, momentum etc.) are thought of as operators in first quantization. The key ideas of this method were introduced in 1927 by Dirac, and were developed, most notably, by Fock and Jordan later.In this approach, the quantum many-body states are represented in the Fock state basis, which are constructed by filling up each single-particle state with a certain number of identical particles. The second quantization formalism introduces the creation and annihilation operators to construct and handle the Fock states, providing useful tools to the study of the quantum many-body theory.
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