College Physics

Permeating frontier progress about two-dimensional materials into the teaching of solid state physics

HUANG Gui-qin

College Physics. 2021, 40(9): 1. doi:10.16854 / j.cnki.1000- 0712.210011

Abstract ( 916 )

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Solid state physics is a course close to the frontiers of science. In this paper，

permeating recent pro- gress of two-dimensional materials into the teaching of solid physics is

discussed. This will make the course contents be full of features of the times and is helpful to stimulate students' enthusiasm for learning and

interest in scientific research.

Variationally optimized orthogonalized associated Laguerre basis applied to calculate exaction energies and wave functions in a freestanding monolayerMoS2

WU Shu-dong, WANG Qiang, CHENG Li-wen

College Physics. 2021, 40(9): 5. doi:10.16854 / j.cnki.1000- 0712.200495

Abstract ( 721 )

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The exaction energies and wave functions in a freestanding monolayer MoS2 are calculated

by an ex- act diagonalization method based on a variationally optimized

orthogonalized associated Laguerre basis. The dielectric screening effect breaks the SO(3)

symmetry， which leads to the fact the exaction energies appear in an a-

nomalous energy ordering of the orbital angular momentum. The method uses associated

Laguerre polynomials to

construct orthogonal basis functions that satisfy both bound and continuum states

automatically and the analytical expressions for the matrix elements of the Hamiltonian are derived. The rate of convergence depends

not only on the number of basis functions but also on the variational parameter. In the case of

variational optimization， the conver- gences are surprisingly fast and show the reliability of

the method. Using the orthogonalized associated Laguerre ba-sis can reduce considerably the basis size and computational cost. Our calculated

eigenenergies with even a small number of basis functions are in excellent agreement with the

results available in the literature. The variationally op- timized orthogonalized associated

Laguerre basis is proven to be suitable for the accurate description of exaction in

two-dimensional materials and atomic physics.

The intuitional teaching method of the beat phenomenon

XIA Zheng-rong, LI Rong-qing, TONG Yue, XU Xiao-xue

College Physics. 2021, 40(9): 10. doi:10.16854 / j.cnki.1000- 0712.200324

Abstract ( 1321 )

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Combining the rotating vector method， the constructed process of the beat phenomenon and

the rea- son that caused the characteristic of the Beat phenomenon are analyzed. Then the

amplitude and the phase position of the beat phenomenon are discussed in detail. Finally， the

phase jump is also shown by the rotating vector method

clearly. The method describing the beat phenomenon in this paper makes the model of the beat

phenomenon so visu-al and intuitive that one can understand it very easily.

Effective potential energy and visualization of rotation of Lagrangian gyro

ZHOU Qun-yi, ZHOU Li-li, MO Yun-fei, HOU Zhao-yang

College Physics. 2021, 40(9): 13. doi:10.16854 / j.cnki.1000- 0712.210078

Abstract ( 1133 )

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In this paper，the energy conservation formula in the article “Analysis of the rotation modes of the

symmetric top around fixed point in gravitational field”has been questioned，and the correct formula has been deduced

and proved. Two conservation parameters are introduced in the formula of effective potential energy，and the

derivative and the second derivative of the effective potential energy are obtained. In addition，the effective potential

energy and second-order derivative have also been calculated when the derivative is zero. Through drawing and analysis，

the range of the change of nutation angle during the gyro rotation and the stability at the equilibrium point

are explained.

How much charges on a hemisphere?

QIU Wei-gang

College Physics. 2021, 40(9): 21. doi:10.16854 / j.cnki.1000- 0712.200546

Abstract ( 1258 )

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The electric potential produced by two hemispheres with constant and opposite potential

is expressed as infinite sums of Legendre functions in spherical coordinate. The electric charge density and total charges on the

hemisphere are derived. Calculation shows that the charge is infinite.

Understanding the equivalent descriptions for polarization and magnetization by analyzing the 　　electromagnetic forces on mediums

PAN Rui, NIE Zhu-yang, LIN Fang, YAO Xin, WANG Lei, ZHANG Xiao-xiao, TANG Yu, JI Zhi-hong,

College Physics. 2021, 40(9): 23. doi:10.16854 / j.cnki.1000- 0712.200509

Abstract ( 876 )

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This article aims to build a connection between the polarized charge distribution and the

electric po- larization density by deriving the electric field force on a medium in two

approaches. One is based on the polarized

charge distribution and the other is based on the electric polarization density. This article

also connects the magneti- zation density and the magnetizing current density by deriving the

magnetic field force on a medium in two approa-ches based on the magnetization density and the magnetizing current density

respectively. The methods used in this article not only show the aforementioned connections， but also directly tell the

relationship between the polarized charge surface density and the electric polarization as

well as the relation between the magnetization density and the magnetizing current surface

density at the boundary of the medium， which is powerful and easy to learn.

Measuring the width of the cut-off part of the Billet split lens by the split-wavefront double-beam interferometry experiment

ZHU Ling, LU Rong-de, ZHAO Wei, ZHENG Hong, ZHANG Quan, LI Heng-yi

College Physics. 2021, 40(9): 28. doi:10.16854 / j.cnki.1000- 0712.200479

Abstract ( 1316 )

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The interferometry of spherical wave convergent light is used in this paper to

experimentally measure the width of the cut- off part of the Billet split lens by using He-

Ne laser as the light source，and the uncertainty

analysis of the width value is carried out.Also，the width value is taken as a known

quantity to obtain the length of the sodium light wave based on the interferometry of plane wave divergent light and spherical wave

convergent light.The experimental data are analyzed to verify the rationality of experimentally measuring the

width of the cut-off part of the Billet split lens.

A calculation method of gravity potential of spherical topography

ZHU Hua-qiang

College Physics. 2021, 40(9): 33. doi:10.16854 / j.cnki.1000- 0712.210127

Abstract ( 826 )

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With the abundance of exploration data of Mars and moon，the traditional

rectangular coordinate gravity potential model is not suitable for the forward and

inverse processing of the gravity of such small bodies. To solve this problem，a

spherical model based on Newton's gravitational is presented，which is expanded by

spherical harmonic expansion.It is shown that the gravity potential of spherical topography can be

estimated by the topography and its higher order spherical harmonic expansion coefficient，which

simplifies the complicated quadrature process of traditional numerical integration.Results also

indicate that the influence of higher topography is less than 7 orders，

and within 5 orders are generally better to meet the accuracy requirements.The algorithm is

applied to the estimation of the gravity potential on the surface of Mars，and the results

are consistent with the topography characteristics of Mars，which shows that the proposed

algorithm is reasonable to some extent.

Exploration and practice of improving teaching and learning quality of college physics experiment based on transfer theory

JIANG Han-yu, HE Jun, DING Zuo-ming, ZHANG Kai-yang, CHU Hong-yan

College Physics. 2021, 40(9): 37. doi:10.16854 / j.cnki.1000- 0712.210125

Abstract ( 756 )

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In order to improve the teaching and learning quality of college physics experiment，a

teaching meth- od based on the transfer theory is proposed in this paper.Preview before class

is performed with the portrait mode of

structuralism to construct a fine knowledge system for the cognitive and attitude

transfer.Inquiry teaching is adopted in the teaching-learning process to improve the

transfer efficiency.Reflection and extension are promoted after class to consolidate the

transfer achievement. The practice has showed that this teaching method fully realizes

the advan-tage of the transfer theory in teaching and learning，stimulates the activity of

students'thinking，makes students′ex- periment process change from simple repetition into

deep understanding，and finally enhances the students'learning capacity and creativity.

Discussion on teaching method of optical simulation design and challenging innovation training

JIANG Ping, YANG Hua-jun, CAIYANG Wei-nan, WU Shao-yi, QIN Yan

College Physics. 2021, 40(9): 42. doi:10.16854 / j.cnki.1000-0712.210017

Abstract ( 773 )

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Based on the training concept of theoretical modeling， visual simulation，

innovative practice and frontier challenges，the teaching team focused on implementing the

training goal of the “Applied Physics Strengthening Foundation Plan” of University of Electronic

Science and Technology of China，and has carried out the reform of prac- tical training teaching

mode for undergraduate core courses，such as optical system design，optical communication tech-

nology， mathematical physics method， etc. In terms of teaching methods， the abstract，

complicated and tedious theoretical models are vividly displayed through 3D visual

simulation，which makes it easier to understand.In program- ming training，innovative design and 3D

reconstruction of optical system are carried out to cultivate students' practical programming

ability.In the challenging practice，the virtual simulation platform of the optical experiment is

constructed to inspire the innovative and challenging thinking of college students. This teaching method

has achieved remarkable teaching effect on training research talents with programming

simulation ability and challenging innovation practice a-bility，and provided talents reserve for science and engineering technology research to fulfil

national strategic demand.

Study on Ampere forces between rectangular and between circular cross-section current-carrying parallel double conductors

ZHANG Sheng-yuan, XU Tian-fu, GUO Fang-xia

College Physics. 2021, 40(9): 47. doi:10.16854 / j.cnki.1000-0712.200505

Abstract ( 880 )

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The distribution of magnetic field in space and Ampere forces on conductors

with different cross - section shapes are of great significance in practical engineering

applications.In this paper，the magnetic field distri-bution of the current-carrying conductor with infinite rectangular cross-section and circular

cross-section is theoret- ically analyzed and calculated，and then the Ampere Forces between

two parallel rectangular cross-section conduc- tors and between two circular cross-section

ones are analyzed，the magnetic field distribution and Ampere force are

simulated by Matlab software.The results show that the magnetic induction lines of the

current-carrying conductors with rectangular cross-section are nearly elliptic，and the Ampere

force between the two parallel rectangular cross- section current-carrying conductors is not

only related to the distance and cross-section size，when the distance and cross-section size are

fixed，it also depends on the direction of placement. When the side length ratio a / b >

1，the Ampere Force is less than that of two circular cross-section conductors with the same area and

current-carrying den- sity.And the smaller the a / b values，the greater the force is.When a / b

<1，the force is greater than that.But with the increase of conductor spacing，the difference of two forces becomes smaller and smaller.

Defining the quasi-period of a Moire fringe using continued fraction expansion

YE Zheng-jun, ZHU Yi-ran, HUANG Ze-jiang, XIA Cheng-jie

College Physics. 2021, 40(9): 52. doi:10.16854 / j.cnki.1000-0712.210085

Abstract ( 1018 )

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A Moire fringe formed by the superposition of two parallel periodic arrays of lines is

not strictly peri- odic， whose approximate periodicity corresponds to best approximations to a

real number. The quasi-periodicity of a

Moire fringe can be rigorously defined by expressing the ratio of the respective periods of

the two arrays in the form of a continued fraction expansion， and its quasi-periods can be

derived by approximating the ratio to convergents of different orders. Meanwhile， the observed

period is the lowest quasi - period with a degree of aperiodicity smaller

than an empirical constant. Based on this direct correspondence between a Moire fringe and

continued fraction of a real number， a set of rigorously-periodic Moire fringes and another set of “worst periodic”

golden-ratio fringes can be identified. The present work connects Moire fringes with the basic

properties of real numbers， and therefore pro- vides new understandings for the Moire fringe

phenomenon， and is of general significance to all sorts of periods su-perposition problems.

Solving time-independent Schrödinger equation by the fourth-order accurate difference method

LIU Zhan-yuan, GUAN Cheng-bo, LU Ying-bo, ZHANG Peng, CONG Wei-yan

College Physics. 2021, 40(9): 58. doi:10.16854 / j.cnki.1000-0712.210063

Abstract ( 1272 )

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In the finite difference calculations of the time-independent Schrödinger

equation， the mostly used difference formula is the central difference formula， which is

accompanied with a truncation error on the second-or- der of step-size. In this paper， the

fourth-order accurate difference formulas of the derivatives are derived by the

five-point polynomial interpolation， and used to solve time - independent Schrödinger

equation in several common potential wells. The numerical results show that， the

fourth - order accurate difference formula has better

convergence and higher precision than the common central difference formula.

Investigate on magnetic levitation phenomenon by magnetic stirrer

LIU Meng-ni , ZHANG Yang-lin , YAN Zhi-yuan , SUN Mei-man , FAN Ting

College Physics. 2021, 40(9): 63. doi: 10.16854 / j.cnki.1000- 0712.200532

Abstract ( 773 )

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The flea in the magnetic stirrer can steadily rise and suspend in the viscous fluid

with the change of the speed of magnetic stirrer. The motion of the flea in magnetic levitation

is analyzed theoretically by means of dy-

namical equation， and the parameters affecting the stable levitation are investigated

experimentally by means of var- iable controlling. The experimental and theoretical results

show that the higher the fluid viscosity coefficient， the lower the suspension height of

the flea. As the driving speed of magnetic stirrer increasing， the flea oscillation angu- lar

velocity ωw strengthened， rotation angular velocity ωs weakens， suspension height decreases;

Smaller flea tended to be more stable in the center， and smaller beakers tended to provide an

initial stable state. When the initial height zb from the bottom of the flea is fixed， the

higher the driving speed， or when the driving speed is fixed， the higher the initial height zb

from the bottom of the flea， the smaller the corresponding swing amplitude.

The two-dimensional eddy current’s feedback and manipulation

LIU Hao-tian , FENG Jie-cheng , KANG Xian-wei

College Physics. 2021, 40(9): 68. doi: 10.16854 / j.cnki.1000- 0712.200512

Abstract ( 506 )

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This article is proposed to research the two-dimensional eddy current’s feedback and

manipulation. First of all， aiming at the most important eddy current detection of

non-destructive detection， the uniqueness of the

solution for the inverse problem is proved， according to the theory of electromagnetic radiation.

Secondly， the theory of eddy detection in industry and some factors that influence eddy

detection are investigated. Lastly， because the Maxwell’ s equations are equivalent

between arbitrary curved coordinate systems and rectangular coordinate systems， by

changing the permeability and the dielectric constant， the coordinate of electromagnetic

field can be changed accordingly， which results in controlling the eddy current field.

Electrodynamic explanation of faraday magneto-optical rotation effect

XIAO Tian-ning, WANG Shuan-hu

College Physics. 2021, 40(9): 72. doi:10.16854 / j.cnki.1000- 0712.210068

Abstract ( 2618 )

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Faraday magneto-optical rotation effect is a phenomenon that applying an external

magnetic field to an isotropic medium will induce the optical rotation property. In this

paper， light is regarded as an electromagnetic wave. By using the method of electrodynamics，

starting from the equation of motion of electrons in an isotropic me- dium under an external

magnetic field， the change of the system caused by the magnetic field will be analyzed. And then

the relative dielectric tensor is obtained， which is solved by combining with Maxwell

equations. By using the simple knowledge of electrodynamics， we can strictly deduce that the

eigenstates of magneto-optical system must be right-handed and left-handed polarization.

Furthermore， we can make readers better understand the source of fara-

day effect in the perspective of eigenvalue problem.

Measurement of liquid diffusion coefficient by digital holographic interferometry based on optical path compensation

　HUANG Zi-shan , LIN Jia-mao , WENG Jia-xuan , DENG Jun-can , CHEN Jun-xu , PENG-li,

College Physics. 2021, 40(9): 76. doi:10.16854 / j.cnki.1000- 0712.210094

Abstract ( 921 )

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The measurement of liquid diffusion coefficient plays an important role in

industrial production. In this paper， based on the optical path compensation method， the

Mach-Zehnder interferometric optical path is used

to measure the liquid diffusion coefficient. The object light and the reference light of a laser

holographic interference path passed through the diffusion groove and the compensation groove

respectively. When the liquid to be measured

diffused in the diffusion groove， the interference pattern would change. The diffusion

coefficient can be obtained by

image processing of two interference patterns at different times by fringe

discrimination method. Wavelet deposing

and frequency-domain filtering are required for image processing. After the interference

patterns at different times are superimposed after filtering， the phase changes are obtained

by phase discretization of the superimposed images using the least square phase unwrapping

algorithm of DCT transform. The liquid phase diffusion coefficient can be

obtained by reading the distance between the maximum concentration changes.

Green functions and their applications to ordinary differential equations

QIAN Guang-yao, YAN Ruo-kun, WANG Ze-xi, ZHENG Shen-zhou

College Physics. 2021, 40(9): 81. doi:10.16854 / j.cnki.1000- 0712.210142

Abstract ( 2514 )

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In this paper， we are devoted to a review of the Green functions and the Green

　　function method for solving the initial and boundary value problems of various ordinary

　　differential equations. For the initial value prob- lem of linear ordinary differential equation

　　of first order， the formula of Green function and the solution represented

　　by Green function are given. For the boundary value problem and initial value problem of linear

　　ordinary differential equation of second order， the calculation of Green function and the

　　solution represented by Green function are shown， respectively. The calculation of Green

　　function and the solution representation by Green function for Sturm-

　　Liouville problem satisfying general initial value conditions are established. For the

　　un-mixed and mixed boundary value problems of linear ordinary differential equations of second

　　order， we also consider how to find Green function and the solution represented by Green

　　function， respectively. Finally， For the boundary value problem of higher or- der linear ordinary

　　differential equations， the Green function and the solution expressed by Green function

　　are ob-

　　tained.

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