Representation of Quantum Field Theory by Elementary Quantum
... generators of the Poincare group, which can thus be represented in the tensor space. Since particles are described by irreducible representations of the Poincare group in quantum field theory [11],[12], the states in tensor space appearing as wave functions in space-time can be considered as states ...
... generators of the Poincare group, which can thus be represented in the tensor space. Since particles are described by irreducible representations of the Poincare group in quantum field theory [11],[12], the states in tensor space appearing as wave functions in space-time can be considered as states ...
Introduction to quantum mechanics, Part II
... becomes negative and therefore would correspond to a negative expectation value of b h(q). If one denotes the wavefunction that belongs to the smallest ...
... becomes negative and therefore would correspond to a negative expectation value of b h(q). If one denotes the wavefunction that belongs to the smallest ...
Many-Body Localization
... • Needs to be local – measure with few-body operators. E.g. compact in real-space ...
... • Needs to be local – measure with few-body operators. E.g. compact in real-space ...
Space, time and Riemann zeros (Madrid, 2013)
... zeros after the first terms, but by a more fundamental difference in the periodic orbits. ...
... zeros after the first terms, but by a more fundamental difference in the periodic orbits. ...
Wave Functions - Quantum Theory Group at CMU
... Any point x, p in the classical phase space represents a possible state of the classical particle. In a similar way, almost every wave function in the space H represents a possible state of a quantum particle. The exception is the state ψ(x) which is equal to 0 for every value of x, and thus has nor ...
... Any point x, p in the classical phase space represents a possible state of the classical particle. In a similar way, almost every wave function in the space H represents a possible state of a quantum particle. The exception is the state ψ(x) which is equal to 0 for every value of x, and thus has nor ...
On the mean-field limit of bosons Coulomb two
... Whenever many particles interact by means of weak two-body potentials, one expects that the potential felt by any one particle is given by an average potential generated by the particle density. In this mean-field regime, one hopes to find that the emerging dynamics is simpler and less encumbered by ...
... Whenever many particles interact by means of weak two-body potentials, one expects that the potential felt by any one particle is given by an average potential generated by the particle density. In this mean-field regime, one hopes to find that the emerging dynamics is simpler and less encumbered by ...
2. Fundamental principles
... This equation determines Ψ(qn , t) uniquely when Ψ(qn , t0 ) is specified at some initial time t0 . Clearly both terms of this equation are linear in Ψ. The superposition principle (T2.9) follows because the Schrödinger equation is both linear and homogeneous. The postulate above implies that the s ...
... This equation determines Ψ(qn , t) uniquely when Ψ(qn , t0 ) is specified at some initial time t0 . Clearly both terms of this equation are linear in Ψ. The superposition principle (T2.9) follows because the Schrödinger equation is both linear and homogeneous. The postulate above implies that the s ...
Functional Analysis for Quantum Mechanics
... Hilbert spaces correspond roughly to the coordinate or phase spaces of classical mechanics. In order to construct an entire physical system, one needs some concept of function or observable. Definition. Let A and B be two normed spaces. An operator is a linear map T : A → B. Remark. At this point on ...
... Hilbert spaces correspond roughly to the coordinate or phase spaces of classical mechanics. In order to construct an entire physical system, one needs some concept of function or observable. Definition. Let A and B be two normed spaces. An operator is a linear map T : A → B. Remark. At this point on ...
Strong time operators associated with generalized
... was derived in the framework for the energy-time uncertainty relation in [KA94]. See also e.g. [Fuj80, FWY80, GYS81-1, GYS81-2]. A strong connection with the decay of survival probability was pointed out by [Miy01], where the weak Weyl relation was introduced and then strong time operators were disc ...
... was derived in the framework for the energy-time uncertainty relation in [KA94]. See also e.g. [Fuj80, FWY80, GYS81-1, GYS81-2]. A strong connection with the decay of survival probability was pointed out by [Miy01], where the weak Weyl relation was introduced and then strong time operators were disc ...
Many-body approaches to studies of electronic systems: Hartree-Fock theory and Density
... However, most quantum mechanical systems of interest in physics consist of a large number of interacting particles. The total number of particles N is usually sufficiently large that an exact solution (viz., in closed form) cannot be found. One needs therefore reliable numerical methods for studying ...
... However, most quantum mechanical systems of interest in physics consist of a large number of interacting particles. The total number of particles N is usually sufficiently large that an exact solution (viz., in closed form) cannot be found. One needs therefore reliable numerical methods for studying ...
Canonically conjugate pairs and phase operators
... Since the pioneering work on quantization of the electromagnetic field, where Dirac1 introduced a phase observable, supposedly conjugate to the number operator N , there has been a long controversy wether a phase operator θ̂ can be constructed which obeys the canonical commutation relation (CCR) [N ...
... Since the pioneering work on quantization of the electromagnetic field, where Dirac1 introduced a phase observable, supposedly conjugate to the number operator N , there has been a long controversy wether a phase operator θ̂ can be constructed which obeys the canonical commutation relation (CCR) [N ...
Fulltext
... The quantum problem of an electron in a constant magnetic field is known as the Landau problem. No wonder, it is a fundamental problem of physics. Landau [1] solved the problem in the famous Landau gauge and he obtained wavefunctions which are plane wave solutions in one direction and harmonic oscil ...
... The quantum problem of an electron in a constant magnetic field is known as the Landau problem. No wonder, it is a fundamental problem of physics. Landau [1] solved the problem in the famous Landau gauge and he obtained wavefunctions which are plane wave solutions in one direction and harmonic oscil ...
The Hilbert Book Model
... described by a linear displacement generator This corresponds to the fact that the probability density distribution has a Fourier transform The swarming conditions result in the capability of the swarm to behave as part of ...
... described by a linear displacement generator This corresponds to the fact that the probability density distribution has a Fourier transform The swarming conditions result in the capability of the swarm to behave as part of ...
The fractional quantum Hall effect: Laughlin wave function, fractional
... rewritten as aeff /lM , where aeff is the effective Bohr radius m∗~e2 / ) is large compared to 1. Actually, for the systems in common use (Si MOSFET’s and GaAs-GaAlAs heterostructures) we have α ≡ aeff /lM ∼ 0.1-0.2 at 1 T, and since α increases only as B 1/2 we would need rather strong magnetic fi ...
... rewritten as aeff /lM , where aeff is the effective Bohr radius m∗~e2 / ) is large compared to 1. Actually, for the systems in common use (Si MOSFET’s and GaAs-GaAlAs heterostructures) we have α ≡ aeff /lM ∼ 0.1-0.2 at 1 T, and since α increases only as B 1/2 we would need rather strong magnetic fi ...
chap3
... return the same value. Example: Stationary states are determinate state of the Hamiltonian H (which is the observable energy). A measurement of the total energy on a particle in the stationary state Ψn is certain to yield the corresponding allowed energy En. ...
... return the same value. Example: Stationary states are determinate state of the Hamiltonian H (which is the observable energy). A measurement of the total energy on a particle in the stationary state Ψn is certain to yield the corresponding allowed energy En. ...
Calculation of C Operator in PT -Symmetric Quantum
... T pT −1 = −p, T xT −1 = x, and T iT −1 = −i. The non-Hermitian Hamiltonian H in (1) is not symmetric under P or T separately, but it is invariant under their combined operation; such Hamiltonians are said to possess space-time reflection symmetry (PT symmetry). We say that the PT symmetry of a Hamil ...
... T pT −1 = −p, T xT −1 = x, and T iT −1 = −i. The non-Hermitian Hamiltonian H in (1) is not symmetric under P or T separately, but it is invariant under their combined operation; such Hamiltonians are said to possess space-time reflection symmetry (PT symmetry). We say that the PT symmetry of a Hamil ...
... self-adjoint may still have a canonical self-adjoint extension. Such is the case for non-negative symmetric operators (or more generally, operators which are bounded below). These operators always have a canonically defined Friedrichs extension and for these operators we can define a canonical funct ...
Quantum Mechanics Lecture 30 Dr. Mauro Ferreira
... asymptotic analysis is if the series terminates at a finite value jmax. cjmax +1 = 0 ...
... asymptotic analysis is if the series terminates at a finite value jmax. cjmax +1 = 0 ...
Multiscale theory of finite-size Bose systems: Implications for collective
... present work we explore this effect, seeking to show how short scale structure increases in intensity as the strength of the interatomic forces increase. In particular, we seek a description wherein the N-atom wave function can be understood as a short lengthscale factor with variability that increa ...
... present work we explore this effect, seeking to show how short scale structure increases in intensity as the strength of the interatomic forces increase. In particular, we seek a description wherein the N-atom wave function can be understood as a short lengthscale factor with variability that increa ...