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1.
We find that in a supersymmetric quantum mechanics (SUSY QM) system, in addition to supersymmetric algebra, an associated SU(2) algebra can be obtained by using semiunitary (SUT) operator and projection operator, and the relevant constants of motion can be constructed. Two typical quantum systems are investigated as examples to demonstrate the above finding. The first example is the quantum system of a nonrelativistic charged particle moving in x-y plane and coupled to a magnetic field along z-axis. The second example is provided with the Dirac particle in a magnetic field. Similarly there exists an SUτ(2) SUσ(2) symmetry in the context of the relativistic Pauli Hamilt onian squared. We show that there exists also an SU(2) symmetry associated with the supersvmmetrv of the Dirac particle.  相似文献   

2.
陈文利  卫高峰 《中国物理 B》2011,20(6):62101-062101
By applying a Pekeris-type approximation to the centrifugal term, we study the spin symmetry of a Dirac nucleon subjected to scalar and vector modified Rosen-Morse potentials. A complicated energy equation and associated two-component spinors with arbitrary spin-orbit coupling quantum number k are presented. The positive-energy bound states are checked numerically in the case of spin symmetry. The relativistic modified Rosen-Morse potential cannot trap a Dirac nucleon in the limiting case α→ 0.  相似文献   

3.
Yue-Liang Wu 《中国物理C(英文版)》2017,41(10):103106-103106
The relativistic Dirac equation in four-dimensional spacetime reveals a coherent relation between the dimensions of spacetime and the degrees of freedom of fermionic spinors. A massless Dirac fermion generates new symmetries corresponding to chirality spin and charge spin as well as conformal scaling transformations. With the introduction of intrinsic W-parity, a massless Dirac fermion can be treated as a Majorana-type or Weyl-type spinor in a six-dimensional spacetime that reflects the intrinsic quantum numbers of chirality spin. A generalized Dirac equation is obtained in the six-dimensional spacetime with a maximal symmetry. Based on the framework of gravitational quantum field theory proposed in Ref. [1] with the postulate of gauge invariance and coordinate independence, we arrive at a maximally symmetric gravitational gauge field theory for the massless Dirac fermion in six-dimensional spacetime. Such a theory is governed by the local spin gauge symmetry SP(1,5) and the global Poincar′e symmetry P(1,5)= SO(1,5) P~(1,5) as well as the charge spin gauge symmetry SU(2). The theory leads to the prediction of doubly electrically charged bosons. A scalar field and conformal scaling gauge field are introduced to maintain both global and local conformal scaling symmetries. A generalized gravitational Dirac equation for the massless Dirac fermion is derived in the six-dimensional spacetime. The equations of motion for gauge fields are obtained with conserved currents in the presence of gravitational effects. The dynamics of the gauge-type gravifield as a Goldstone-like boson is shown to be governed by a conserved energy-momentum tensor, and its symmetric part provides a generalized Einstein equation of gravity. An alternative geometrical symmetry breaking mechanism for the mass generation of Dirac fermions is demonstrated.  相似文献   

4.
Negative energy density and the quantum inequality are examined for the Dirac field. A proof is given of the quantum inequality for negative energy densities in the massive Dirac field produced by the superposition of two single particle electron states.  相似文献   

5.
6.
M.  Hamzavit  A.  A.  Rajabi 《中国物理 B》2013,(9):214-216
The Cornell potential that consists of Coulomb and linear potentials has received a great deal of attention in particle physics. In this paper, we present the exact solutions of the Dirac equation with the pseudoscalar Cornell potential under spin and pseudospin symmetry limits. The energy eigenvalues and corresponding eigenfunctions are given in closed form.  相似文献   

7.
The ground-state phase transition and the phonon dispersion relation of the quantum double-well model are studied by means of the time-dependent variational approach combined with a Hartree-type many-body trial wavefunction. The single-particle state is taken to be a frozen Jackiw-Kerman wavefunction. Under the condition of minimum uncertainty relation, we obtain an effective classical Hamiltonian for the system and equations of motion for the particle's expectation values. It is shown that the effective substrate potential transits from a symmetric double-well potential to a symmetric single-well potential, and the ground state exhibits a transition from a broken symmetry phase to a restored symmetry phase as increasing the strength of quantum fluctuations. We also obtain the phonon dispersion relations and the phonon gaps at the two phases.  相似文献   

8.
Two schemes for teleporting an unknown one-particle state are proposed when a general W state is utilized as quantum channel. In the first scheme, after the sender (Alice) makes a Bell-state measurement on her particles, the recipient (Bob) performs a Von Neumann measurement and introduces an auxiliary particle, and carries out a unitary transformation on his particle and the auxiliary particle, and performs a Von Neumann measurement on the auxiliary particle to confirm whether the teleportation succeeds or not. In the second scheme, the recipient (Bob) does not need to perform the first Von Neumann measurement or introduce the auxiliary particle, which is necessary in the first scheme. It is shown that the maxima/probabilities of successful teleportation of the two schemes are identical if the recipient (Bob) performs an appropriate unitary transformation and adopts a proper particle on which he recovers the quantum information of state to be teleported.  相似文献   

9.
An approximate solution of the Dirac equation for a spin-1/2 particle under the influence of q-deformed hyperbolic P ¨oschl–Teller potential combined with trigonometric Scarf II non-central potential is studied analytically. It is assumed that the scalar potential equals the vector potential in order to obtain analytical solutions. Both radial and angular parts of the Dirac equation are solved using the Nikiforov–Uvarov method. A relativistic energy spectrum and the relation between quantum numbers can be obtained using this method. Several quantum wave functions corresponding to several states are also presented in terms of the Jacobi Polynomials.  相似文献   

10.
李志远 《中国物理 B》2014,(11):206-218
A distinct method to show a quantum object behaving both as wave and as particle is proposed and described in some detail. We make a systematic analysis using the elementary methodology of quantum mechanics upon Young's two-slit interferometer and the Mach-Zehnder two-arm interferometer with the focus placed on how to measure the interference pattern (wave nature) and the which-way information (particle nature) of quantum objects. We design several schemes to simultaneously acquire the which-way information for an individual quantum object and the high-contrast interference pattern for an ensemble of these quantum objects by placing two sets of measurement instruments that are well separated in space and whose perturbation of each other is negligibly small within the interferometer at the same time. Yet, improper arrangement and cooperation of these two sets of measurement instruments in the interferometer would lead to failure of simultaneous observation of wave and particle behaviors. The internal freedoms of quantum objects could be harnessed to probe both the which-way information and the interference pattern for the center-of-mass motion. That quantum objects can behave beyond the wave-particle duality and the complementarity principle would stimulate new conceptual examination and exploration of quantum theory at a deeper level.  相似文献   

11.
Based on the opinion that the γ-matrices in Dirac equation have structure and are decomposable, we decompose the γ-matrices into the direct product of the operators in the spin space and the particle-antiparticle space. By using this method, we attain a complete set of commutative operators, a set of quantum numbers and the correspondingly eigen solutions of the Hamiltonian for a charged Dirac particle moving in a uniform constant magnetic field. In addition, the dynamic supersymmetry of the Hamiltonian is unveiled. Spin symmetry breaking and particle-antiparticle symmetry breaking are discussed, and the supersymmetric group operator of the degenerate spin subspace resulting from the spin residual supersymmetry is found.  相似文献   

12.
A modified version of the Feynman relativistic chessboard model (FCM) is investigated in which the paths involved are spirals in space-time. Portions of the paths in which the particle's proper time is reversed are interpreted in terms of antiparticles. With this interpretation the particle-antiparticle field produced by such trajectories provides a classical analog of the phase associated with particle paths in the unmodified FCM. It is shown that in the nonrelativistic limit the resulting kernel is the correct Dirac propagator and that particle-antiparticle symmetry is in this case responsible for quantum interference.  相似文献   

13.
We find that in a supersymmetric quantum mechanics (SUSY QM) system, in addition to supersymmetric algebra, an associated SU(2) algebra can be obtained by using semiunitary (SUT) operator and projection operator, and the relevant constants of motion can be constructed. Two typical quantum systems are investigated as examples to demonstrate the above finding. The first example is the quantum system of a nonrelativistic charged particle moving in x-y plane and coupled to a magnetic field along z axis. The second example is provided with the Dirac particle in a magnetic field. Similarly there exists an SUτ(2) \otimes SUσ(2) symmetry in the context of the relativistic Pauli Hamiltonian squared. We show that there exists also an SU(2) symmetry associated with the supersymmetry of the Dirac particle.  相似文献   

14.
NG Sarkar  S Biswas  A Shaw 《Pramana》1999,53(4):685-700
We study the behaviour of Dirac current in expanding spacetime with Schrödinger and de Sitter form for the evolution of the scale-factor. The study is made to understand the particle-antiparticle rotation and the evolution of quantum vacuum leading to particle production in such spacetime.  相似文献   

15.
Several years ago, in quantum mechanics, Davies proposed a method to calculate particle’s traveling time with the phase difference of wave function. The method is convenient for calculating the sojourn time inside a potential step and the tunneling time through a potential hill. We extend Davies’ non-relativistic calculation to relativistic quantum mechanics, with and without particle-antiparticle creation, using Klein–Gordon equation and Dirac Equation, for different forms of energy-momentum relation. The extension is successful only when the particle and antiparticle creation/annihilation effect is negligible.  相似文献   

16.
17.
It is proposed to study the particle-antiparticle symmetry in a ring accommodating protons and antiprotons simultaneously. Experiments to measure a possible proton-antiproton mass difference, and to test the Dirac theory and CPT theorem, are discribed.  相似文献   

18.
Two models for the production of particles with internal quantum numbers are investigated. They are based on the leading particle approximation. First a unitary isospin invariant S-operator model is constructed for pion production. Then generalized coherent states for particle-antiparticle pairs are introduced from which a statistical operator is derived. Both approaches imply non-vanishing correlation integrals.  相似文献   

19.
An algebraic block-diagonalization of the Dirac Hamiltonian in a time-independent external field reveals a charge-index conservation law which forbids the physical phenomena of the Klein paradox type and guarantees a single-particle nature of the Dirac equation in strong external fields. Simultaneously, the method defines simpler quantum-mechanical objects—paulions and antipaulions, whose 2-component wave functions determine the Dirac electron states through exact operator relations. Based on algebraic symmetry, the presented theory leads to a new understanding of the Dirac equation physics, including new insight into the Dirac measurements and a consistent scheme of relativistic quantum mechanics of electron in the paulion representation. Along with analysis of the mathematical anatomy of the Klein paradox falsity, a complete set of paradox-free eigenfunctions for the Klein problem is obtained and investigated via stationary solutions of the Pauli-like equations with respective paulion Hamiltonians. It is shown that the physically correct Dirac states in the Klein zone are characterized by the total particle reflection from the potential step and satisfy the fundamental charge-index conservation law.  相似文献   

20.
根据Heisenberg对应原理(HCP),在经典极限下厄密算符的量子矩阵元对应经典物理量的Fourier展开系数.将HCP应用到相对论领域的Dirac方程中,对于自由粒子和在匀磁场中的带电粒子,其量子算符的矩阵元在经典极限下对应着相对论物理方程的解.计算表明,在经典极限下量子期望值就是对应经典物理量的时间平均值.  相似文献   

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