A detailed procedure based on an analytical transfer matrix method is presented to solve bound-state problems. The derivation is strict and complete. The energy eigenvalues for an arbitrary one-dimensional potential c...A detailed procedure based on an analytical transfer matrix method is presented to solve bound-state problems. The derivation is strict and complete. The energy eigenvalues for an arbitrary one-dimensional potential can be obtained by the method. The anharmonic oscillator potential and the rational potential are two important examples. Checked by numerical techniques, the results for the two potentials by the present method are proven to be exact and reliable.展开更多
In this paper, the analytical transfer matrix method (ATMM) is applied to study the properties of quantum reflection in three systems: a sech2 barrier, a ramp potential and an inverse harmonic oscillator. Our resul...In this paper, the analytical transfer matrix method (ATMM) is applied to study the properties of quantum reflection in three systems: a sech2 barrier, a ramp potential and an inverse harmonic oscillator. Our results agree with those obtained by Landau and Lifshitz [Landau L D and Lifshitz E M 1977 Quantum Mechanics (Non-relativistic Theory) (New York: Pergamon)], which proves that ATMM is a simple and effective method for quantum reflection.展开更多
The purpose of this study was to investigate the effect of bolt profile on load transfer mechanism of fully grouted bolts in jointed rocks using analytical and numerical methods. Based on the analytical method with de...The purpose of this study was to investigate the effect of bolt profile on load transfer mechanism of fully grouted bolts in jointed rocks using analytical and numerical methods. Based on the analytical method with development of methods, a new model is presented. To validate the analytical model, five different profiles modeled by ANSYS software. The profile of rock bolts T3 and T4with load transfer capacity,respectively 180 and 195 kN in the jointed rocks was selected as the optimum profiles. Finally, the selected profiles were examined in Tabas Coal Mine. FLAC analysis indicates that patterns 6+7 with2 NO flexi bolt 4 m better than other patterns within the faulted zone.展开更多
This paper investigates the photon tunneling and transmittance resonance through a multi-layer structure including a left-handed material(LHM). An analytical expression for the transmittance in a five-layer structur...This paper investigates the photon tunneling and transmittance resonance through a multi-layer structure including a left-handed material(LHM). An analytical expression for the transmittance in a five-layer structure is given by the analytical transfer matrix method. The transmittance is studied as a function of the refractive index and the width of the LHM layer. The perfect photon tunneling results from the multi-layer structure, especially from the relation between the magnitude of the refractive index and the width of the LHM layer and those of the adjoining layers. Photons may tunnel through a much greater distance in this structure. Transmittance resonance happens, the peaks and valleys appear periodically at the resonance thickness. For an LHM with inherent losses, the perfect transmittance is suppressed.展开更多
This paper applies the analytical transfer matrix method (ATMM) to calculate energy eigenvalues of a particle in low dimensional sharp confining potential for the first time, and deduces the quantization rules of th...This paper applies the analytical transfer matrix method (ATMM) to calculate energy eigenvalues of a particle in low dimensional sharp confining potential for the first time, and deduces the quantization rules of this system. It presents three cases in which the applied method works very well. In the first quantum dot, the energy eigenvalues and eigenfunction are obtained, and compared with those acquired from the exact numerical analysis and the WKB (Wentzel, Kramers and Brillouin) method; in the second or the third case, we get the energy eigenvalues by the ATMM, and compare them with the EBK (Einstein, Brillouin and Keller) results or the wavefunction outcomes. From the comparisons, we find that the semiclassical method (WKB, EBK or wavefunction) is inexact in such systems.展开更多
This paper studies quantum reflection with recent research on reflection coefficient. Based on the analytical transfer matrix method, a novel explanation for this phenomenon is proposed that quantum reflection is the ...This paper studies quantum reflection with recent research on reflection coefficient. Based on the analytical transfer matrix method, a novel explanation for this phenomenon is proposed that quantum reflection is the reflection of subwaves, which originate inherently from the inhomogeneity of the fields and is always neglected in the semiclassical regime. Comparison with exact formula and the numerical calculations for different potentials has confirmed the reliability and the validity of the proposed theory.展开更多
This paper obtains a generalized tunneling time of one-dimensional potentials via time reversal invariance. It also proposes a simple explanation for the Hartman effect using the useful concept of the scattered subwaves.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 60877055 and 60806041)the Shanghai Rising-Star Program,China (Grant No. 08QA14030)+1 种基金the Innovation Funds for Graduates of Shanghai University,China (Grant No. SHUCX092021)the Foundation of the Science and Technology Commission of Shanghai Municipality,China (Grant No. 08JC14097)
文摘A detailed procedure based on an analytical transfer matrix method is presented to solve bound-state problems. The derivation is strict and complete. The energy eigenvalues for an arbitrary one-dimensional potential can be obtained by the method. The anharmonic oscillator potential and the rational potential are two important examples. Checked by numerical techniques, the results for the two potentials by the present method are proven to be exact and reliable.
基金Project supported by Science Foundation of Nantong University (Grant Nos. 03080122 and 09ZY001)
文摘In this paper, the analytical transfer matrix method (ATMM) is applied to study the properties of quantum reflection in three systems: a sech2 barrier, a ramp potential and an inverse harmonic oscillator. Our results agree with those obtained by Landau and Lifshitz [Landau L D and Lifshitz E M 1977 Quantum Mechanics (Non-relativistic Theory) (New York: Pergamon)], which proves that ATMM is a simple and effective method for quantum reflection.
文摘The purpose of this study was to investigate the effect of bolt profile on load transfer mechanism of fully grouted bolts in jointed rocks using analytical and numerical methods. Based on the analytical method with development of methods, a new model is presented. To validate the analytical model, five different profiles modeled by ANSYS software. The profile of rock bolts T3 and T4with load transfer capacity,respectively 180 and 195 kN in the jointed rocks was selected as the optimum profiles. Finally, the selected profiles were examined in Tabas Coal Mine. FLAC analysis indicates that patterns 6+7 with2 NO flexi bolt 4 m better than other patterns within the faulted zone.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 60877055 and 60806041)the Innovation Funds for Graduates of Shanghai University,China (Grant No. SHUCX102016)
文摘This paper investigates the photon tunneling and transmittance resonance through a multi-layer structure including a left-handed material(LHM). An analytical expression for the transmittance in a five-layer structure is given by the analytical transfer matrix method. The transmittance is studied as a function of the refractive index and the width of the LHM layer. The perfect photon tunneling results from the multi-layer structure, especially from the relation between the magnitude of the refractive index and the width of the LHM layer and those of the adjoining layers. Photons may tunnel through a much greater distance in this structure. Transmittance resonance happens, the peaks and valleys appear periodically at the resonance thickness. For an LHM with inherent losses, the perfect transmittance is suppressed.
文摘This paper applies the analytical transfer matrix method (ATMM) to calculate energy eigenvalues of a particle in low dimensional sharp confining potential for the first time, and deduces the quantization rules of this system. It presents three cases in which the applied method works very well. In the first quantum dot, the energy eigenvalues and eigenfunction are obtained, and compared with those acquired from the exact numerical analysis and the WKB (Wentzel, Kramers and Brillouin) method; in the second or the third case, we get the energy eigenvalues by the ATMM, and compare them with the EBK (Einstein, Brillouin and Keller) results or the wavefunction outcomes. From the comparisons, we find that the semiclassical method (WKB, EBK or wavefunction) is inexact in such systems.
基金supported by the National Natural Science Foundation of China (Grant Nos.10874121 and 60677029)
文摘This paper studies quantum reflection with recent research on reflection coefficient. Based on the analytical transfer matrix method, a novel explanation for this phenomenon is proposed that quantum reflection is the reflection of subwaves, which originate inherently from the inhomogeneity of the fields and is always neglected in the semiclassical regime. Comparison with exact formula and the numerical calculations for different potentials has confirmed the reliability and the validity of the proposed theory.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10874121 and 60677029)
文摘This paper obtains a generalized tunneling time of one-dimensional potentials via time reversal invariance. It also proposes a simple explanation for the Hartman effect using the useful concept of the scattered subwaves.