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1 Uncertainty principle and position operator in standard theory
1 Uncertainty principle and position operator in standard theory

... quantum theory should reproduce the motion of a particle along the classical trajectory defined by classical equations of motion. Hence the position operator is needed only in semiclassical approximation and it should be defined from additional considerations. In summary, one should start from momen ...
Quantum statistics: Is there an effective fermion repulsion or boson
Quantum statistics: Is there an effective fermion repulsion or boson

... Our intention is not to be critical of authors for using the words “repulsion” and “attraction” in describing the statistical effects of wavefunction antisymmetry or symmetry. This concept has been with physics since the early days of quantum mechanics. Nevertheless, it is important to examine the u ...
slides
slides

... the Hilbert space of cylindrical functions defined on a graph which contains a number of loops such the one introduced by the action of the Euclidean part of .Which means that each loop is associated to a pair of links originating from the same node. ...
ThesisPresentation
ThesisPresentation

Quantum statistics: Is there an effective fermion repulsion or boson
Quantum statistics: Is there an effective fermion repulsion or boson

... partition function, and its contribution already is accounted for in the classical ideal gas pressure; it cancels out in Eq. 共13兲. The second term corrects the incorrect classical momentum distribution represented by the first term. The classical term includes double-occupation states; for fermions ...
Many-body theory
Many-body theory

... large number of particles. The reason is the equivalence of particles, a genuine quantum effect, which requires the (anti)symmetrization of the wave functions. The resulting wave functions are too complicated for any useful calculation. Another representation of the many particle system, based on th ...
Coherent State Path Integrals
Coherent State Path Integrals

... Therefore the path integral for a system of non-relativistic bosons (with chemical potential µ) has the same form os the path integral of the charged scalar field we discussed before except that the action is first order in time derivatives. th fact that the field is complex follows from the require ...
Some Notes on Field Theory
Some Notes on Field Theory

... number of degrees of freedom. Examples are systems of many interacting particles or critical phenomena like second order phase transitions. Here we will concentrate on the scattering of particles, but the general framework can be applied to any domain in physics. For an introduction, we simplify Nat ...
The wave function and particle ontology - Philsci
The wave function and particle ontology - Philsci

... The above analysis can be extended to an arbitrary entangled wave function for an N-body system. Since each physical entity is only in one position in space at each instant, it may well be called particle. Here the concept of particle is used in its usual sense. A particle is a small localized objec ...
Creation and Destruction Operators and Coherent States
Creation and Destruction Operators and Coherent States

... Coherent States Coherent states are an important class of states that can be realized by any system which can be represented in terms of a harmonic oscillator, or sums of harmonic oscillators. They are the answer to the question, what is the state of a quantum oscillator when it is behaving as clas ...
幻灯片 1 - Yonsei
幻灯片 1 - Yonsei

... For equal mass system, because of the difference of charge conjugation quantum number, the vector states can be distinguished by the charge conjugation, so the physical states are But for non-equal mass system, there is no the quantum number of charge conjugation, so we can not separate these two st ...
Schroedinger equation Basic postulates of quantum mechanics
Schroedinger equation Basic postulates of quantum mechanics

... Postulates of Quantum Mechanics A ) For every “classical” observable a linear operator. It can depend on momentum and position operators. Momentum operator (x) is proportional to derivative over x ...
Table des mati`eres 1 Technical and Scientific description of
Table des mati`eres 1 Technical and Scientific description of

... There is a lot of combinatorial features which look like the classical case (often at the cost of replacing numbers and factorials and Rook numbers [54] by their q-analogues). Here, in spite of the existence of the q-derivative which, with the multiplication by x satisfies the (12) relation, the ric ...
Deriving new operator identities by alternately using normally
Deriving new operator identities by alternately using normally

... will probably be increasingly used in the future as it becomes better understood and its own special mathematics gets developed [1].” Following his expectation, the technique of integration within an ordered product (IWOP) of operators was invented which can directly apply the Newton-Leibniz integra ...
Equidistant spectra of anharmonic oscillators
Equidistant spectra of anharmonic oscillators

Lecture8
Lecture8

... represent the operators Hˆ , aˆ, aˆ  , etc., and even xˆ and pˆ , as matrices. Since m aˆ  n  n  1 if m = n+1 and vanishes otherwise, we can represent â  as an infinite matrix: ...
Green’s Functions Theory for Quantum Many-Body Systems Many-Body Green’s Functions
Green’s Functions Theory for Quantum Many-Body Systems Many-Body Green’s Functions

... Green’s function can be defined in any single-particle basis (not just r or k space). So let’s call {α} a general orthonormal basis with wave functions {uα(r)} ...
Outline of section 4
Outline of section 4

... We have now seen three ways of thinking about the Uncertainty principle: (1) As the necessary disturbance of the system due to measurements (e.g. the Heisenberg microscope) (2) Arising from the properties of Fourier transforms (narrow spatial wavepackets need a wide range of wavevectors in their Fou ...
7 Angular Momentum I
7 Angular Momentum I

... This is true because J+ |µmax , νi = 0. Then, we can substitute J− J+ with Eq. (17) and get ν = j(j + 1). Applying J+ to the state with a maximal value of µ we should get 0. But we can apply J− . If we apply it k-times the final state will be proportional to |j − k, νi. This state also should satisf ...
Quantum states in phase space • classical vs. quantum statistics
Quantum states in phase space • classical vs. quantum statistics

... Equations (6.10) and (6.15) are effectively mutual inversions. We can interpret this result as a one-to-one correspondence between the density operator �ˆ and the (c-number) phasespace function W (α). Both contain exactly the same information about the quantum state of the system. The knowledge of th ...
Complex symmetric operators
Complex symmetric operators

... other means [16]). Here H is an infinite Hankel matrix and S is the unilateral ...
Combinatorics and Boson normal ordering: A gentle introduction
Combinatorics and Boson normal ordering: A gentle introduction

... Hilbert space constitutes the arena where quantum phenomena can be described. One common realization is Fock space, which is generated by the set of orthonormal vectors |ni representing states with a specified numbers of particles or objects. A particular role in this description is played by the cr ...
Short-time-evolved wave functions for solving quantum many
Short-time-evolved wave functions for solving quantum many

Quantum field theory and Green`s function
Quantum field theory and Green`s function

... The reason why it is hard to write down wavefunctions for indistinguishable particles is because when we write do the wavefunciton, we need to specify which particle is in which quantum state. For example, yi r j  means the particle number j is in the quantum state yi . This procedure is natural f ...
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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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