Continuum states of modified Morse potential

Wei, G.; Wen-Li, Chen

doi:10.1088/1674-1056/19/9/090308

Cited by 15 publications

(13 citation statements)

References 25 publications

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“…The spectrum is defined in such a way that states with negative energy are bound and states with zero or positive energy are unbound. For a discussion on the unbound states and spectrum, see, for example [36][37][38]. The bound state conditions imply that the quantum numbers n, m may take the following values [39] n, m ∈ {0, 1, .…”

Section: Initial and Partner Morse Hamiltoniansmentioning

confidence: 99%

Coherent states of the two-dimensional non-separable supersymmetric Morse potential

Moran

Hussin

2021

Eur. Phys. J. Plus

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Supersymmetry is a fundamental feature of a quantum theory described by a supersymmetric Hamiltonian comprised of several quantum mechanical Hamiltonians with different potentials that allows us to relate information about the states and spectra of the constituent Hamiltonians. In this paper we reconstruct Ioffe's set of states for the singular non-separable two-dimensional Morse potential using supersymmetry from a non-degenerate set of states constructed for the initial separable Morse Hamiltonian. We define generalised coherent states, compute their uncertainty relations, and we find that the singularity in the partner Hamiltonian significantly affects the localisation of the coherent state wavefunction.

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Section: Initial and Partner Morse Hamiltoniansmentioning

confidence: 99%

Coherent states of the two-dimensional non-separable supersymmetric Morse potential

Moran

Hussin

2021

Eur. Phys. J. Plus

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“…[1−13] As mentioned in Refs. [3][4][5][6][7], when the train density of railway line reaches a certain degree, it will form the train traffic flow and the trains interact with each other. Accordingly, some characteristics of train traffic flow, including the traffic capacity, velocity, etc., can be analyzed drawing on the experience of macroscopic traffic flow theory for road traffic flow on the base of numerical results.…”

Section: Introductionmentioning

confidence: 99%

“…Up to now, many models and methods have been proposed to depict train movements, including cellular automata (CA) model, [1][2][3][4][5]13] discrete-time model (DTM), [6][7]14] discrete-event model (DEM), [8][9][10]16] carfollowing model, [15] etc. In 2005, Li et al [1−2] firstly applied CA theory to the railway system by changing update rules.…”

Section: Introductionmentioning

confidence: 99%

“…Xu et al [5] developed an equation of minimum safety headway under moving block system to depict train movements and some characteristics of train traffic flow were captured. Along with the development of CA theory, a discrete-time movement model (DTM) was introduced by Yang et al [6] by taking the stochastic disturbances of train traffic flow into consideration, but only the homogeneous train traffic flow was discussed in their work. By utilizing the DTM, Sun et al [7] simulated the mixed high-speed train movements on double-track railway line and analyzed some characteristics of railway traffic flow.…”

Section: Introductionmentioning

confidence: 99%

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An Improved Discrete-Time Model for Heterogeneous High-Speed Train Traffic Flow

Xu¹,

Jia²,

Li³

et al. 2016

Commun. Theor. Phys.

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This paper aims to present a simulation model for heterogeneous high-speed train traffic flow based on an improved discrete-time model (IDTM). In the proposed simulation model, four train control strategies, including departing strategy, traveling strategy, braking strategy, overtaking strategy, are well defined to optimize train movements. Based on the proposed simulation model, some characteristics of train traffic flow are investigated. Numerical results indicate that the departure time intervals, the station dwell time, the section length, and the ratio of fast trains have different influence on traffic capacity and train average velocity. The results can provide some theoretical support for the strategy making of railway departments.

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“…In their approach, the speed varied in sections when different strategies were adopted. Yang et al [19] proposed a simulation method based on a discrete-time model under stochastic disturbance. Wang et al [20] analyzed the properties of the rail traffic flow under the moving block system and presented the simulation of train scheduling based on the CA model.…”

Section: Introductionmentioning

confidence: 99%

Scheduling of high-speed rail traffic based on discrete-time movement model

Sun¹,

Cao²,

Yan³

et al. 2013

Chinese Phys. B

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In this paper, a new simulation approach for solving the mixed train scheduling problem on the high-speed double-track rail line is presented. Based on the discrete-time movement model, we propose control strategies for mixed train movement with different speeds on a high-speed double-track rail line, including braking strategy, priority rule, travelling strategy, and departing rule. A new detailed algorithm is also presented based on the proposed control strategies for mixed train movement. Moreover, we analyze the dynamic properties of rail traffic flow on a high-speed rail line. Using our proposed method, we can effectively simulate the mixed train schedule on a rail line. The numerical results demonstrate that an appropriate decrease of the departure interval can enhance the capacity, and a suitable increase of the distance between two adjacent stations can enhance the average speed. Meanwhile, the capacity and the average speed will be increased by appropriately enhancing the ratio of faster train number to slower train number from 1.

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Continuum states of modified Morse potential

Cited by 15 publications

References 25 publications

Coherent states of the two-dimensional non-separable supersymmetric Morse potential

Coherent states of the two-dimensional non-separable supersymmetric Morse potential

An Improved Discrete-Time Model for Heterogeneous High-Speed Train Traffic Flow

Scheduling of high-speed rail traffic based on discrete-time movement model

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