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Table of Content

    20 December 2018 Volume 37 Issue 12
      
    Quantum control of time-dependent magnetic field on the electron spin
    LUO Guo-zhong
    College Physics. 2018, 37(12):  1.  doi:10.16854 /j.cnki.1000-0712.180071
    Abstract ( 2076 )   PDF (200KB) ( 496 )  
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    The quantum control of the time varying magnetic field on the electron spin is studied by means of

    the method for the quantum control of the electron spin in a constant magnetic field,namely,the time varying magnetic

    field is converted to a rotating magnetic field and a constant magnetic field. Using the precession frequency of

    the rotating magnetic field and the adjustment of magnitude and action time of the magnetic field,it can make the

    spin direction of the particle cause periodic change occurred between the +z and -z directions and adjust the size of

    amplitude of the static magnetic field and the time of action to control the spin of the electron. This achieves the

      control of the direction of electron spin.

    AB effect and transport operator based on the mechanical momentum
    WANG Xin, LIU Tian-gui, LIU Quan-hui
    College Physics. 2018, 37(12):  4.  doi:10.16854 /j.cnki.1000-0712.180125
    Abstract ( 1371 )   PDF (274KB) ( 578 )  
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    In the presence of a magnetic field,the momentum can be classified into mechanical and canonical

    one,where the mechanical momentum corresponds to the velocity,and quantum mechanics has seldem introduced

    the transport operator via the mechanical momentum. When the AB effect is discussed,the dynamical method is

    uaually invoked. Once the transport operator is formed and is taken round the trips circuiting the magnetic field,AB

    effect is reproduced. Our method explicitly exhibits the geometrical nature of the AB effect.

    Three representations in quantum mechanics
    WANG Huai-yu
    College Physics. 2018, 37(12):  7.  doi:10.16854 /j.cnki.1000-0712.180323
    Abstract ( 3375 )   PDF (213KB) ( 848 )  
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    The formalisms of the three representations in quantum mechanics are introduced. They are

    Schrdinger representation,Heisenburg representation and interaction representation. The mistakes in some text

    books and their reasons are pointed out. A correct expression between the time evolution operators in the

    Schrdinger and interaction representations is given. The expression in some text books is wrong because the initial

    time is set as zero. The time-dependent perturbation formula is derived.

    Research on forced vibration mode for a square plate with free boundary
    YAN Qi-qi, CHEN Yan, HU Xiang
    College Physics. 2018, 37(12):  11.  doi:10.16854 /j.cnki.1000-0712.180134
    Abstract ( 1442 )   PDF (988KB) ( 596 )  
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    The forced vibration mode for a square plate with free boundary is studied. Its displacement solution

    is assumed to a Fourier series,which is plugged into the corresponding control equation and boundary conditions to

    solve the unknown displacement coefficient by using the orthogonality of trigonometric function. Then displacement

    solutions under different frequencies are calculated and the corresponding nodal charts can be drawn. The results

    show that the nodal charts of simulation and the Cladni patter of experimental observations match very well,and the

    corresponding frequency values of theoretical calculation and the experiment observation are also very closed,which

    prove that the displacement solution is efficient and accurate.

    Study of electric properties of 3×n Fan network
    TAN Zhi-zhong, WU Peng, LUO Xiao-lian, KONG Ze-lin
    College Physics. 2018, 37(12):  16.  doi:10.16854 /j.cnki.1000-0712.180162
    Abstract ( 935 )   PDF (531KB) ( 213 )  
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    Similarity and difference between strong and weak quantum measurement theory
    Taximaiti Yusufu, Yusuf Turek
    College Physics. 2018, 37(12):  22.  doi:10.16854 /j.cnki.1000-0712.170704
    Abstract ( 2291 )   PDF (211KB) ( 1157 )  
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    From the viewpoint of definition,features and applications aspects,we briefly discuss the similarity

    and difference between strong and weak quantum measurement theories.

    Study of homoclinic orbits and quasi-period behavior of atomic chain in the one-dimensional Frenkel-Kontorova model
    KANG Ju, HUANG Tou-sheng, MENG Tian-xiang, ZHANG Hua-yong
    College Physics. 2018, 37(12):  26.  doi:10.16854 /j.cnki.1000-0712.180230
    Abstract ( 1238 )   PDF (1911KB) ( 272 )  
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    The dynamic behaviors of homoclinic orbits,multi-period oscillation and quasi-period oscillation of

    an atomic chain are investigated by the one-dimensional Frenkel-Kontorova model. Firstly,the hyperbolic saddle

    focus existed in the system is decided by the eigenvalues of Jacobian matrix. Secondly,the condition of system generation

    homoclinic orbits is determined via Silnikov theorem at the hyperbolic saddle focus. Finally,the numerical

    simulation is used to verify the existence of homoclinic orbits,multi-period oscillation and quasi-period oscillation

    of the system. The results of this paper also provide a valuable reference for the study of solid friction phenomena.

    Research on parity measurement in optical Mach-Zehnder interferometer
    WANG Shuai, PEI Ming-xu, ZHU Xiao-qin
    College Physics. 2018, 37(12):  30.  doi:10.16854 /j.cnki.1000-0712.180046
    Abstract ( 2008 )   PDF (243KB) ( 529 )  
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    Mach-Zehnder interferometer is an important optical device in quantum precision measurement.Considering

    a general two-mode quantum pure state as a probe state,by using the Dirac symbol and the theory of

    quantum representation transformation,we present a simple method to calculate the expectation value of parity operator

    in the output state of a Mach-Zehnder interferometer.

    Coherent state representation of optical beam splitter operator and its application
    LI Heng-mei, YUAN Hong-chun, WANG Zhen, WAN Zhi-long
    College Physics. 2018, 37(12):  33.  doi:10.16854 /j.cnki.1000-0712.180321
    Abstract ( 1877 )   PDF (239KB) ( 692 )  
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    Optical beam splitter ( BS) is one of the basic linear elements in quantum optics,which is widely

    used in the preparation of quantum states.Based on the matrix transformation relation of BS,we derive the natural

    representation of BS operator in the coherent state representation.Then,its normally form can be concisely deduced

    by virtue of the technique of integration within ordered product ( IWOP) .Furthermore,as an application of coherent

    state representation of BS operator,we conveniently derive the output state of multiphoton catalysis with coherent

    state input.Compared with other methods,this method is easier and neater.

    Theoretical and error analysis of Millikan’s oil-drop experiment
    YANG Jin-song, ZENG Da-peng, CHEN Jie
    College Physics. 2018, 37(12):  37.  doi:10.16854 /j.cnki.1000-0712.180275
    Abstract ( 10821 )   PDF (535KB) ( 1511 )  
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    Millikan and his student designed the oil-drop experiment,which plays an important role in the history

    of physics,to reveal that magnitude of any charged bodies takes separation value,and determine magnitude of

    the electron’s change. Suitable choices for oil-drop will help us to improve the measuring accuracy. Some books about

    physical experiment provided choice rules,however it is not explained the reasons why we shall make that

    choices. In this paper,we focus on choice rules for the oil-drop experiment,and reveal the physical reasons by

    combining theoretical and error analysis. These results presented in this paper will provide theoretical support for

    choice rules of oil-drop.

    The teardrop and heart-like rotating catenary
    ZHANG Zi-jin, SUN Xiao-lin, HUANG Jing, QIU Wei-gang
    College Physics. 2018, 37(12):  41.  doi:10.16854 /j.cnki.1000-0712.180120
    Abstract ( 1397 )   PDF (631KB) ( 433 )  
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    A uniform mass distributed rotating chain can take a teardrop configuration with both ends fixed at

    the same point. It also can take an upside down heart like configuration with two ends fixed separately in a vertical

    rod when the angular velocity and separated distance are well chosen. The experimental figures agree well with the

    theoretical curves.

    Study of the stable state and breakage of the liquid between two parallel flat plates
    DU Fan, CHEN Zong-qiang, CHEN Jing, YU Hua, LIU Song-fen, CAO Xue-wei
    College Physics. 2018, 37(12):  44.  doi:10.16854 /j.cnki.1000-0712.180092
    Abstract ( 1253 )   PDF (1387KB) ( 296 )  
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    The liquid forms into liquid bridges between bodies which are close to each other,and tends to pull

    the bodies to get nearer. The structure and stability of the liquid bridge are mainly determined by the structure of

    solid,the characters of liquid and solid,as well as the temperature. The energy variation method is used to figure out

    the stable state of the liquid bridge,which allows the force between liquid and solid to be accurately calculated,under

    both static and quasi-static circumstance. Taking thin liquid structure between glass plates for instance,the fast

    breakage process of large area liquid bridges are discussed,and fractal phenomenon,fingering phenomenon and inhomogeneous

    shrink in this process are analyzed. The liquid bridges have significant effects on micro electro mechanical

    system and bio-adhesion.

    Numerical and approximate analytical solutions of the eigen-value equation for the one-dimensional finite square well
    YANG Zi-qian, MIAO qing, FAN Zhuan-zhuan, CHEN Peng, LV ming, JIN Guang-ri
    College Physics. 2018, 37(12):  49.  doi:10.16854 /j.cnki.1000-0712.180255
    Abstract ( 4065 )   PDF (552KB) ( 1267 )  
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    The bound states of one-dimensional finite square well cannot be solved exactly. Numerically,the

    energy spectrum and its wave function can be obtained from a transcendental equation. In this paper,we solve the

    transcendental equation with the Taylor series expansion,which to the first order gives analytical solutions of the energy

    spectrum and its wave function. We find that the number of bound states is determined by a dimensionless parameter

    R,which is proportional to the width of the well multiplied by the square of the potential height. Except the highest

    level wave function,the approximate analytical results show in well agreement with the numerical results. In the

    limit of large R,the approximate analytical results recover the exactly solvable problem of an infinite square well.

    Why trains stay on tracks
    B.Shayak
    College Physics. 2018, 37(12):  53.  doi:10.16854 /j.cnki.1000-0712.180573
    Abstract ( 1679 )   PDF (924KB) ( 738 )  
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    In this article,we give both qualitative and quantitative explanations of why a train stays on itstrack, in spite of

    perturbations that could cause it to derail.We show that train stability originatesfrom the conical shape of the

    wheels,which gives rise to a restoring normal force in response to alateral disturbance.We first demonstrate translational

    stabilization in a simple situation where therails are assumed frictionless and the steering motion of the wheel

    is neglected.We then develop amore comprehensive model, taking friction and steering into account.We show that

    rolling frictioncouples the rotational motion to the translational motion,enhancing overall stability.Finally,we find

    approximate formulae for the parameters governing stability,and show good agreement withparameters of a real railway

    coach.