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Table of Content
20 August 2019 Volume 38 Issue 8
Several notes on the momentum correlation function of a Brownian particle
BAO Jing-dong
College Physics. 2019, 38(8): 1. doi:
10.16854 /j.cnki.1000-0712.180599
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The momentum correlation functuin is a very important physical quantity in non-equilibrium statistical mechanics.However，where are a few errors for the explain of this function and related contents in our usual textbooks.This paper starts from academic research and discusses those un-rigorous descriptions.The Langevin equation subjected to a white noise is regarded as a model in the present textbooks，but it is difficulty for clearing two characteristic times in the Brownian motion: the correlation time of random force and relaxation time of system.This paper solves this question in terms of the generalized Langevin equation with an Ornstein-Uhlenbeck colored noise. The ergodicity of the momentum variable is studied by using the Khinchin theorem and thus the cost of the momentum correlation function is deepen.
A further discussion on collision problems
LU Jun-ling, GU Chen, QIN Lian-hua, REN Nai-jing, MA Bo-yi
College Physics. 2019, 38(8): 5. doi:
10.16854 /j.cnki.1000-0712.180535
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1978
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Studying one-dimensional free collision of two small balls in the velocity space can directly find that the centroid system is a special inertial reference system.The most possible kinetic energy loss caused by collision is the total kinetic energy of two small balls in this centroid system ( corresponding to completely inelastic collision) . The kinetic energy loss of general inelastic collision is only a part of the total kinetic energy，and its proportional coefficient. It is related to Newton's coefficient of recovery ( the ratio of relative velocity before and after collision) .The results show that the concept of one-dimensional free collision of a sphere can be extended to the collision with a rigid body，and the reciprocal of the equivalent reduced mass of the collision is equal to the sum of the reciprocal of the characteristic parameters of the objects involved in the collision. The Newton recovery coefficient formula obtained by dividing the separation velocity by the approaching velocity is generally valid， in which the separation velocity and the approaching velocity refer to the velocity of the collision points on two objects.Two-dimensional collisions can be represented by a composite process of a major collision ( relative velocity zero crossing) and an adjoin collision ( relative velocity no more than zero) orthogonal to it.
A supplement to the article“Electric field in the cavity of a charged thick ellipsoidal shell”
YU Feng-jun, YANG Yu-peng, WEI Ke-wei, ZHANG Xi-wei
College Physics. 2019, 38(8): 10. doi:
10.16854 /j.cnki.1000-0712.180644
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1332
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We calculate the electric potential inside the cavity of a uniformly charged thick ellipsoidal shell. This shell is composed of non-conductor.Its inner and outer surfaces are two coaxial ellipsoidal surfaces with the same eccentricity ratios.The electric potential in the cavity is calculated by using the comparison method and the superposition principle of the electric potential，and the electric potential in the center of the uniformly charged ellipsoid is obtained by the way.
An improved method to explain the diamagnetism of materials
GUO Ran
College Physics. 2019, 38(8): 14. doi:
10.16854 /j.cnki.1000-0712.180656
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1357
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In order to make an understandable illustration for undergraduate students，an improved method of explaining the diamagnetism of materials is suggested.First， the mechanism of the diamagnetism is interpreted by theoretical derivations when the orbital magnetic moment of electron is parallel to the external magnetic field.And then， the properties of the motion of electron is analyzed by employing numerical calculations in the case of orbital magnetic moment of electron not parallel to the external magnetic field.The numerical results are illustrated and displayed as figures，which reveal the mechanism of the diamagnetism in this case.
Time-evolution operator approach to free particle in quantum mechanics
ZHANG Yin-jie, YAN Yu-li
College Physics. 2019, 38(8): 19. doi:
10.16854 /j.cnki.1000-0712.180639
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2680
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The evolution of one-dimensional free particle is calculated by using time-evolution operator. The evolution of the variance of one-dimensional free particle wave packet is calculated，the results show that the wave packet spreads over time. Using the annihilation operator，the evolution of wave function of Gaussian wave packet is calculated，here the Gaussian wave packet is a“stationary”wave packet located at the origin at the initial time. A series expression is obtained，sum it up the elementary function expression is obtained，the spreading of the wave packet in time has been directly confirmed.
Analysis of the incomplete ionization of impurities in semiconductors
HUANG Hai-meng
College Physics. 2019, 38(8): 21. doi:
10.16854 /j.cnki.1000-0712.190016
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2977
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The incomplete ionization of impurities in semiconductors is one of the key and difficult points in the course of Physics of Semiconductor. By the profound analysis on the incomplete ionization of impurities，this paper deduces the relationship among the four essential parameters of the ionization rate η，the temperature T，the doping concentration ND and the ionized energy ΔED. Furthermore，the maximum doping concentration for complete ionization as well as the dependence of the ionization rate upon the ionized energy are proposed，and the introduction of the Lambert W-function simplifies the solution of temperature. Moreover，the issue of the incomplete ionization in 4H-SiC is discussed. The discussions and conclusions are beneficial for the students to have the systematic comprehension on the basic problems concerning incomplete ionization of impurities，and to develop the ability of analysis and innovation for future research and design work in the fields of semiconductor devices.
Analysis of the measurement of acoustic velocity through an acoustic controlled standing wave tube
ZHANG Bo, LIU Xiang-yuan, ZHAO Min-fu, FANG Jie, ZHANG Gang, KONG Min, YUAN Hao
College Physics. 2019, 38(8): 26. doi:
10.16854 /j.cnki.1000-0712.180560
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1934
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The acoustic controlled standing wave tube is composed of a transparent acrylic tube，a unit lighting array controlled by acoustic wave，a acoustic wave transducer and a hard end cover and holders. When the acoustic wave signals are provided to the acoustic wave transducer，the similar standing wave states are formed in the transparent acrylic tube due to the wave superposition. The theoretical analysis has shown that this standing wave has wave nodes and loops and is in agreement with that of the ideal standing wave. Therefore，this standing wave tube can be used to measure the wavelength of acoustic waves. With the acoustic controlled standing wave tube，by carefully adjusting the frequency and amplitude of the acoustic wave signals，the wave nodes and loops are able to be clearly displayed by the LED brightness. The experimental results have revealed that the measurement of acoustic velocity with such standing wave tube has advantages of accuracy and simplicity for operators.
Research on the associated effects in Hall effect and the measurement of the horizontal component of the geomagnetic filed
XU Lei, FANG Li-qing, XIAO Shan, WU Bo, MAO Jie-jian
College Physics. 2019, 38(8): 30. doi:
10.16854 /j.cnki.1000-0712.190005
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Different associated effects have the influence on the Hall voltage measured in the experiment of Hall effect，such as the Ettinghausen，Nernst，Righi-Ledue，IR drop，thermoelectric drop. In fact，geomagnetic filed also has the effect on the measurement of the Hall voltage. This study has shown that these associated effects could be eliminated by the method of symmetric measurement except the Ettinghausen effect. The influence of IR drop is prominent，and the influence of thermoelectric drop and Geomagnetic filed effects take the second place，while the contributions of the Nernst and Righi-Ledue effects could be ignored. Moreover，the Horizontal component of the geomagnetic filed in Shangrao，measured by the experiment of Hall effect，is about 30.6 μT.
Research on measuring Boltzmann constant based on ampere-volt characteristic of PN junction
QI Ling-min, HAN Tai-kun, HU Su-mei, CHEN Hai-bo, HE Yan
College Physics. 2019, 38(8): 39. doi:
10.16854 /j.cnki.1000-0712.180681
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According to the principle of measuring Boltzmann constant based on the ampere-volt characteristic of PN junction，the diode and triode are used as the substitute samples of PN junction in the experiments. The result has shown that the Boltzmann constant measured directly by the diode is larger than the theoretical value which is inconsistent with the results in some literatures. Then the reason is analyzed based on the factors of diffusion current， recombination current and surface current. The Boltzmann constant measured by using the base-level circuit composed of triode is relatively more accurate because of the influence of recombination current and surface current being reduced.
Optimization of the measurment of optical wavelength by the method of grating least deviation angle
LIANG Xiong, LAI Guo-zhong
College Physics. 2019, 38(8): 42. doi:
10.16854 /j.cnki.1000-0712.190030
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1700
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The judgment uncertainty existing in the least deviation angle method is about the same as the minimum resolution angle of the spectrometer’s telescope in the grating diffraction experiment. By using the characteristic that the diffracted light reaches the minimum deviation angle and is parallel to the reflected beam，the method of judging the minimum deviation angle is improved by means of orthogonal mirrors. Thus，theoretically，the judgment uncertainty could be reduced and the measurement error achieved in the symmetrical measurement method could be further reduced to half of that done by the single-sided method. The experimental result has shown that this method is feasible.
Measuring electric field-strain effect by Michelson interferometer
GONG De-wei, WANG Xiao-ou, ZHAO Yuan
College Physics. 2019, 38(8): 46. doi:
10.16854 /j.cnki.1000-0712.180667
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The method of Michelson interference in the optical part of college physics is applied to the measurement of electric field -strain effect. The experimental principle of electric field - strain effect measurement using Michelson interference is analyzed. The electric field-strain effect of LiNbO3 crystal is measured experimentally and the factors affecting the measurement accuracy is analyzed. The results have shown that the method of Michelson interference can be used to measure electric field-strain effect very well.
Detection of core cuttings surface morphology by terahertz wave
QIN Fan-kai, ZHAN Hong-lei, BAO Ri-ma, ZHAO Kun, CHEN Xing-jie, LV Xin
College Physics. 2019, 38(8): 50. doi:
10.16854 /j.cnki.1000-0712.180630
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The surface morphology and crude oil distribution of natural core and artificial core cuttings are detected by a reflective terahertz spectral imaging system，and the results of sample analysis with scanning electron microscope complemented each other and confirmed each other. Due to the distribution of pores and minerals，the terahertz time-domain spectral ( THz-TDS) amplitudes at different locations have significant differences，and the difference in THz-TDS amplitude decreases after filling the pores with crude oil. This experiment combines the new optical method of terahertz technology and the knowledge related to petroleum geology，which can stimulate students’scientific research interest and cultivate innovative spirit.
College physics teaching reform — quantum communication teaching analysis
ZHANG Zi-jing, WANG Xiao-ou, HUO Lei, ZHANG Yu, ZHAO Yuan
College Physics. 2019, 38(8): 54. doi:
10.16854 /j.cnki.1000-0712.180615
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Under the background that the education reform of new times and new engineering is imperative，combining with the characteristics of college physics teaching in our engineering-dominated university，the reform of“college physics teaching system of new times and new engineering”is proposed. The new times require engineering graduates to better understand modern cutting - edge technologies. On the basis of the original college physics teaching，we have expanded a series of new technologies related to modern physics. This paper takes quantum communication technology as an example. Quantum communication is a new cross technology which combines quantum physics and classical communication. Due to the features of“indivisibility”，“uncertainty”and“No-Cloning Theorem”， quantum communication can realize unconditional security， making it a new security communication technology. As one of the quantum technologies，quantum communication has always given people the feeling of“Unattainablez”，which makes non-professional people flinch. This paper is just to explain the basic principles of quantum communication in a simple way. These new technologies are added into the old college physics teaching，making college physics closer to the frontier technology.
Solution of constraint reaction force on non-smooth orbit and numerical calculation and analysis by Mathematica software
YE Zhi-qiang, GUO Qin
College Physics. 2019, 38(8): 59. doi:
10.16854 /j.cnki.1000-0712.180584
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1478
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648
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In engineering design，the supporting force of the orbit to the object is often taken into consideration， and the non-smooth orbit is closest to the physical reality. This paper studies the constraint force problem of the small ring constrained on the non-smooth orbit. By using the differential equation of particle motion，the analytical solution of the constraint reaction of a small ring at any position on the parabolic orbit is obtained. At the same time，the effect of friction on the motion process of small ring is studied. And the numerical calculations and analysis of the complete process of forward and return movement is performed with the help of Mathematica software. The example of solving this kind of problem is given. The solution technique of the non-smooth orbit problem can be applied to other forms of orbits.
On chemical potentials of atoms and phonons in Einstein solid model
PENG Jun-bo, CHEN Qing, LIU Quan-hui
College Physics. 2019, 38(8): 63. doi:
10.16854 /j.cnki.1000-0712.180669
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In general，for a thermodynamic system each thermodynamic function has only one expression. However，solid has two chemical potentials，one for solid atoms and another for phonons，which have finite and vanishing value，respectively. Einstein utilized the Boltzmann statistics to discuss the heat capacity of the solid especially at low temperature，in which the partition function for single oscillating degree of freedom of the solid atoms can as well be intepreted on the base of phonon gas. It is evident that the chemical potential for the solid atoms can not be taken to be that of the phonon gas. How to simultaneouly determine the values of both chemical potentials is explicitly illustrated with microcanonical ensemble.
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