College Physics

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 ( 2252 )

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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 ( 1517 )

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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 ( 3695 )

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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 ( 1642 )

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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 ( 1063 )

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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 ( 2511 )

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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 ( 1383 )

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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 ( 2213 )

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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 ( 2058 )

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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 ( 12028 )

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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 ( 1520 )

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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 ( 1393 )

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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 ( 4535 )

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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 ( 1826 )

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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.

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