The analysis and calculating method of dynamic errors of CMMs during probing are discussed.To relate the dynamic displacement errors with the dynamic rotational errors a method for obtaining the displacement errors at...The analysis and calculating method of dynamic errors of CMMs during probing are discussed.To relate the dynamic displacement errors with the dynamic rotational errors a method for obtaining the displacement errors at the probing position from dynamic rotational errors is presented.It is pointed out that the finite element method might be used for modeling dynamic errors.However,dynamic errors are difficult to be modeled so a combined practical and theoretical approach is needed.In addition,the dynamic errors are measured with inductive position sensors.展开更多
The principle and accuracy of 3-D coordinates acquisition using one single camera and the Aided Measuring Probe(AMP) are discussed in this paper. Using one single camera and one AMP which has several embedded targets ...The principle and accuracy of 3-D coordinates acquisition using one single camera and the Aided Measuring Probe(AMP) are discussed in this paper. Using one single camera and one AMP which has several embedded targets and one tip with known coordinates, the single camera′s orientation and location can be calculated. After orientation, the global coordinate system is obtained. During measurement, the camera is fixed firstly, then the AMP is held and the feature point is touched.The camera is triggered lastly. The position and orientation of the AMP are therefore calculated from the size and position of its image on the sensor. Since the tip point of AMP has known relation with the embedded targets, the feature point can be measured. Tests show that the accuracy of length measurement is 0.2 mm and accuracy for flatness measurement in XSY-plane is 0.1 mm.展开更多
By virtue of the technique of integration within an ordered product of operators, we derive the normal ordering expansion of a one- and two-mode combination squeezing operator for two harmonic oscillators with coordin...By virtue of the technique of integration within an ordered product of operators, we derive the normal ordering expansion of a one- and two-mode combination squeezing operator for two harmonic oscillators with coordinate- momentum coupling. It turns out that this squeezing operator just diagonalizes the Hamiltonian H=p^21/2m1＋m1ω^21x^21/2＋p^222m2＋m2ω^22x^22/2-λx2p1 so its ground state is a one- and two-mode combination squeezed state. Quantum fluctuation in the ground state is calculated.展开更多
We introduce bivariate normal distribution operator for state vector [ψ） and find that its marginal distribution leads to one-dimensional normal distribution corresponding to the measurement probability ｜λ,v〈x｜...We introduce bivariate normal distribution operator for state vector [ψ） and find that its marginal distribution leads to one-dimensional normal distribution corresponding to the measurement probability ｜λ,v〈x｜.ψ〉｜^2, where ｜x〉λ,v is the coordinate-momentum intermediate representation. As a by-product, the one-dimensional normal distribution in statistics can be explained as a Radon transform of two-dimensional Gaussian function.展开更多
Usually the Virial theorem,which can be derived from the Feynman-Hellmann theorem,applies to Hamil-tonians without coordinates-momentum coupling.In this paper we discuss when there are such kind of couplings inHamilto...Usually the Virial theorem,which can be derived from the Feynman-Hellmann theorem,applies to Hamil-tonians without coordinates-momentum coupling.In this paper we discuss when there are such kind of couplings inHamiltonians then how the Virial theorem should be modified.We also discuss the energy contribution arising from thecoordinates-momentum coupling for a definite energy level.展开更多
We discuss the unitary operator corresponding to the general two-mode coordinate-momentum mixed transformation(q2,p2)→(Aq1+Bq2,Cq1+Dp2),where A,B,C and Dare arbitrary real numbers,Suitably selecting the parameters A,...We discuss the unitary operator corresponding to the general two-mode coordinate-momentum mixed transformation(q2,p2)→(Aq1+Bq2,Cq1+Dp2),where A,B,C and Dare arbitrary real numbers,Suitably selecting the parameters A,B,Cand D,we obtain a new two-mode bosonic realization of the SU(1,1) Lie algebra.We also study the squeezing effects of the squeezed vacuum associated with the new two-mode bosonic realization of the SU(1,1) Lie algebra.The results show that the new squeezed vacuum does not possess second-order squeezing,but exhibits higher-order squeezing.展开更多
We present a convenient approach to finding multi-partite entangled state with continuum variables, which is the common eigenvectors of center-of-mass coordinate and mass-weighted relative momenta, by decomposing the ...We present a convenient approach to finding multi-partite entangled state with continuum variables, which is the common eigenvectors of center-of-mass coordinate and mass-weighted relative momenta, by decomposing the normally ordered Gaussian-form operator expressing the completeness relation which is constructed by analyzing the eigenvector equations. The whole derivation is based on the technique of integration within an ordered product of operators.展开更多
The generalized Virial theorem for mixed state, derived from the generalized Hellmann Feynman theorem, only applies to Hamiltonians in which potential of coordinates is separate from momentum energy term. In this pape...The generalized Virial theorem for mixed state, derived from the generalized Hellmann Feynman theorem, only applies to Hamiltonians in which potential of coordinates is separate from momentum energy term. In this paper we discuss Virial theorem for mixed state for some Hamiltonians with coordinate-momentum couplings in order to know their contributions to internal energy.展开更多
文摘The analysis and calculating method of dynamic errors of CMMs during probing are discussed.To relate the dynamic displacement errors with the dynamic rotational errors a method for obtaining the displacement errors at the probing position from dynamic rotational errors is presented.It is pointed out that the finite element method might be used for modeling dynamic errors.However,dynamic errors are difficult to be modeled so a combined practical and theoretical approach is needed.In addition,the dynamic errors are measured with inductive position sensors.
文摘The principle and accuracy of 3-D coordinates acquisition using one single camera and the Aided Measuring Probe(AMP) are discussed in this paper. Using one single camera and one AMP which has several embedded targets and one tip with known coordinates, the single camera′s orientation and location can be calculated. After orientation, the global coordinate system is obtained. During measurement, the camera is fixed firstly, then the AMP is held and the feature point is touched.The camera is triggered lastly. The position and orientation of the AMP are therefore calculated from the size and position of its image on the sensor. Since the tip point of AMP has known relation with the embedded targets, the feature point can be measured. Tests show that the accuracy of length measurement is 0.2 mm and accuracy for flatness measurement in XSY-plane is 0.1 mm.
文摘By virtue of the technique of integration within an ordered product of operators, we derive the normal ordering expansion of a one- and two-mode combination squeezing operator for two harmonic oscillators with coordinate- momentum coupling. It turns out that this squeezing operator just diagonalizes the Hamiltonian H=p^21/2m1＋m1ω^21x^21/2＋p^222m2＋m2ω^22x^22/2-λx2p1 so its ground state is a one- and two-mode combination squeezed state. Quantum fluctuation in the ground state is calculated.
基金supported by National Natural Science Foundation of China under Grant No.10574647
文摘We introduce bivariate normal distribution operator for state vector [ψ） and find that its marginal distribution leads to one-dimensional normal distribution corresponding to the measurement probability ｜λ,v〈x｜.ψ〉｜^2, where ｜x〉λ,v is the coordinate-momentum intermediate representation. As a by-product, the one-dimensional normal distribution in statistics can be explained as a Radon transform of two-dimensional Gaussian function.
基金the Specialized Research Fund for the Doctorial Progress of Higher Education of China under Grant No.20070358009
文摘Usually the Virial theorem,which can be derived from the Feynman-Hellmann theorem,applies to Hamil-tonians without coordinates-momentum coupling.In this paper we discuss when there are such kind of couplings inHamiltonians then how the Virial theorem should be modified.We also discuss the energy contribution arising from thecoordinates-momentum coupling for a definite energy level.
文摘We discuss the unitary operator corresponding to the general two-mode coordinate-momentum mixed transformation(q2,p2)→(Aq1+Bq2,Cq1+Dp2),where A,B,C and Dare arbitrary real numbers,Suitably selecting the parameters A,B,Cand D,we obtain a new two-mode bosonic realization of the SU(1,1) Lie algebra.We also study the squeezing effects of the squeezed vacuum associated with the new two-mode bosonic realization of the SU(1,1) Lie algebra.The results show that the new squeezed vacuum does not possess second-order squeezing,but exhibits higher-order squeezing.
基金Supported by the National Natural Science Foundation of China under Grant No. 10874174the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No. 20070358009
文摘We present a convenient approach to finding multi-partite entangled state with continuum variables, which is the common eigenvectors of center-of-mass coordinate and mass-weighted relative momenta, by decomposing the normally ordered Gaussian-form operator expressing the completeness relation which is constructed by analyzing the eigenvector equations. The whole derivation is based on the technique of integration within an ordered product of operators.
文摘The generalized Virial theorem for mixed state, derived from the generalized Hellmann Feynman theorem, only applies to Hamiltonians in which potential of coordinates is separate from momentum energy term. In this paper we discuss Virial theorem for mixed state for some Hamiltonians with coordinate-momentum couplings in order to know their contributions to internal energy.
