College Physics

Calculation of collective vibrational modes of ions trapped in a multi-trap system by solving Lagrange equation

. 2011, 30(4): 1-1.

Abstract ( 594 )

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The basic method for calculating the collective vibrational modes of ions trapped in a multi-trap system is presented by solving Lagrange equation and the vibrational modes of three ions trapped in the multi-trap system are calculated concretely.

The key position of light velocity in the theory of relativity

. 2011, 30(4): 4-4.

Abstract ( 606 )

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In this paper,we introduce the important role of the postulate about light velocity in the empty space,which is not only the foundation of the theory of relativity,but also enables us define the simultaneity of time and distance of space.

Completeness and nodes of eigenfunctions for a class of unconventional Sturm-Liouville eigenvalue problem

. 2011, 30(4): 8-8.

Abstract ( 672 )

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The vibration of a string or a rod with their ends connected to particles（concentrated mass）,orsimilar problems,result in a class of unconventional Sturm-Liouville eigenvalue problem after separation of variables.The completeness of the eigenfunctions of such eigenvalue problems is proved.It is also proved that the n-th eigenfunction has n-1 nodes（zeros）.

Analysis on a free vibration system of many identical pendulums

. 2011, 30(4): 12-12.

Abstract ( 659 )

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The differential equation of motion of the system with many identical pendulums is derived by using Lagrange＇ equation.Based on properties of three diagonal matrixes,the recursion expressions of characteristic polynomial and mode vectors of the vibration system are given.Moreover,taking three identical pendulums as examples,we show the application of the result and confirm the result in the reference [3] with this method.

The rotating rope with mass hanged on the end

. 2011, 30(4): 16-16.

Abstract ( 603 )

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The equation of rotating rope with an object hanging on the end in the stable state is derived.The normal angular speed under which the rope can rope stable is calculated numerically under the boundary conditions.The dependence of normal angular speed on the mass of hanging object is discussed.The comparison between theoretical and experimental figures is also performed.

Research on the problem of burst for pressure

. 2011, 30(4): 19-19.

Abstract ( 543 )

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Based on the mechanics analysis,we explain the burst reason of water tube and water crock at the time of ice expand,and the reason of burst of vault is also discussed.

A sample solution of the dynamic equation of special relativity

. 2011, 30(4): 22-22.

Abstract ( 602 )

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A concise solution of the dynamic equation of special relativity is presented for a particle acted by a constant force.The acceleration,velocity and equation of motion are expressed by simple functions,the differences and relations between special relativity and Newton＇s dynamics are analyzed in detail.

Compression invariance of the charge distribution of an ellipsoidal conductor at the principal axes

. 2011, 30(4): 25-25.

Abstract ( 641 )

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A new characteristic of the charge distribution of an ellipsoidal conductor is given,namely,the compression invariance at the principal axes.

The compact theory of the mathematical tools about the expression forms of the electromagnetic inductive law

. 2011, 30(4): 28-28.

Abstract ( 751 )

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According to compact mathematical theory,we apply three kinds of methods to deduce the motional-induced expression from the flux expression of the electromagnetic inductive law.Thus it is claer that if on interval of [t,t＋dt） the loop does not break,the two expression forms will be equivalence at the moment of t.The mathematical theory about the rates of flux and circulation versus time is given.It is pointed out that the order of integral operation and differential operation should be exchanged.

Study of diffraction fields of Fresnel zone plate based on wavefront phase factor

. 2011, 30(4): 33-33.

Abstract ( 777 )

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Based on the method of wavefront phase-factor and considering of the influence of limited aperture of zone plate,we analyse the diffraction fields by Fresnel zone plate which contains three components.The corresponding integral expressions of the diffraction fields are given,the formulae of the amplitude distribution of diffraction fields alone axis are presented and a series of curves are shown.Finally,the transverse line-width and the axial line-width of that real focal-spot are obtiained.This study may further provide a theoretical foundation to optical element by Fresnel zone plate.

Numerical simulation of square hole Fraunhofer diffraction

. 2011, 30(4): 38-38.

Abstract ( 1114 )

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Based on the Huygens-Fresnel principle,the square hole Fraunhofer diffraction is simulated numerically.The theory of diffraction is verified,the diffraction patterns of non-axis space and small square hole are also obtained.This can expand the concepts of diffraction and provide a reference for better undersatnding of diffraction.

Planck’s theory about＂Geometrical optics of non-homogeneous bodies relationships to quantum mechanics＂

. 2011, 30(4): 43-43.

Abstract ( 625 )

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The theory about how Planck presenting the stationary Schrdinger equation by the analogy between geometrical optics equations in non-homogeneous bodies with fundamental equations of classical mechanics for a free particle,which moves in a given static conservative field of force,is introduced.

A simple method to calculate mutual inductance between two coaxial circularcoils in general situation

. 2011, 30(4): 46-46.

Abstract ( 859 )

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The series expansion method is used to get the exact infinite series expression of the mutual inductance between two coaxial circular coils in general situation.The infinite series is convergent in all cases except for the two coils coincide with each other.Moreover,vector potential,instead of magnetic induction,is used to calculate the magnetic flux,which makes the method more convenient.

Measuring the stretch sensitivity of piezoelectric ceramic by confocal spherical scanning interferometer

. 2011, 30(4): 49-49.

Abstract ( 614 )

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The paper introduces a new way to measure the stretch sensitivity of piezoelectric ceramic.We use the helium-neon gas laser＇s analysis apparatus to measure the voltage increment of corresponding sequence＇s two adjacent interference lines and calculate the elongation.This process can be used to measure expediently and accurately the sensitivity of piezoelectric ceramics convenient.

Eigenfunction on isosceles right triangle with hybrid boundary condition

. 2011, 30(4): 52-52.

Abstract ( 663 )

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It is assumed that the eigenfunction on isosceles right triangle with hybrid boundary condition is a linear combination of eight plane-wave functions.The eight coefficients are settled from the boundary condition.

A teaching investigation on the basic concept of quantum mechanics

. 2011, 30(4): 54-54.

Abstract ( 662 )

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The meanings of superposition principle and uncertainty principle are discussed by using the dynamic model of one-dimensional potential well.The doubts about the static model of quantum tunneling effects are pointed out and a dynamic model of tunneling effects is also proposed.The micro-mechanism of tunneling effects is discussed.

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