Tunneling of a diatomic molecule with unbound states in one dimension

Shegelski, Mark R. A.; Hnybida, Jeff; Friesen, H.; Lind, Crystal; Kavka, Jeremy J

doi:10.1103/physreva.77.032702

Cited by 13 publications

(23 citation statements)

References 18 publications

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“…The justification for use of a δ barrier has been verified in our previous publications [9][10][11][12][13], where we showed that the δ barrier gives an excellent approximation for more realistic barriers, such as rectangular barriers and Gaussian barriers. By substituting (15) into (11), we find that the effective potential for a molecule incident upon a δ barrier is given by…”

Section: A Formulation Of the Problemsupporting

confidence: 66%

“…In previous work involving time-independent analysis [9][10][11][12][13], Schrödinger equations similar to (8) were derived, and formal solutions to the equations were obtained using Green's function methods. From those formal solutions, the reflection and transmission probabilities were obtained using a method developed by Razavy [14].…”

Section: A Formulation Of the Problemmentioning

confidence: 99%

“…Choosing b/a = 1.0775, we have f 0 = −0.0001186, f 1 = 0.001046, f 2 = 0.003223, and f 3 = 0.006489. The method used to obtain these values is presented in [11].…”

Section: A Formulation Of the Problemmentioning

confidence: 99%

“…Ultimately, it would be desirable to extend our investigation of time-dependent tunneling to include a higher number of states and to include the continuum of unbound states (such as in Ref. [11]). Additionally, it would be of interest to see how molecular straddling changes upon increasing the value of the molecular interaction range, L/a.…”

Section: Future Workmentioning

confidence: 99%

“…Tunneling of a diatomic molecule incident upon a potential barrier in one and three dimensions was reported in [9] and [10]. The case of a molecule with a continuum of unbound states incident upon a potential barrier was considered in [11]. An investigation into the tunneling of a molecule with many bound states was reported in [12].…”

Section: Introductionmentioning

confidence: 99%

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Quantum tunneling and reflection of a molecule with a single bound state

2010

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In this article, we present the results of studies on the quantum mechanical tunneling and reflection of a diatomic, homonuclear molecule with a single bound state incident upon a potential barrier. In the first study, we investigate the tunneling of a molecule using a time-dependent formulation. The molecular wave function is modeled as a Gaussian wave packet, and its propagation is calculated numerically using Crank-Nicholson integration. It is found that a molecule may transition between the bound state and an unbound state numerous times during the process of reflection from or transmission past the barrier. It is also found that, in addition to reflecting and transmitting, the molecule may also temporarily straddle the potential barrier in an unbound state. In the second study, we consider the case of a molecule incident in the bound state upon a step potential with energy less than the step. We show that in the limit where the binding energy e 0 approaches zero and the step potential V 0 goes to infinity, the molecule cannot remain in a bound state if the center of mass gets closer to the step than an arbitrarily large distance x 0 which increases as the magnitude of e 0 decreases, as V 0 increases, or both. We also show that, for e 0 → 0 − and V 0 → ∞, if the molecule is incident in the bound state, it is reflected in the bound state with probability equal to unity, when the center of mass reaches the reflection distance x 0 . We verify that the unbound states exhibit the expected physical behavior. We discuss some surprising results. Connections between our results and investigations done in cold atoms, excitons, Cooper pairs, and Rydberg atoms are discussed.

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Section: A Formulation Of the Problemsupporting

confidence: 66%

Section: A Formulation Of the Problemmentioning

confidence: 99%

“…Choosing b/a = 1.0775, we have f 0 = −0.0001186, f 1 = 0.001046, f 2 = 0.003223, and f 3 = 0.006489. The method used to obtain these values is presented in [11].…”

Section: A Formulation Of the Problemmentioning

confidence: 99%

Section: Future Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum tunneling and reflection of a molecule with a single bound state

2010

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One Dimensional Time-Dependent Tunnelling of Excitons

et al. 2017

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Transmission and reflection of a molecule with a dipole moment incident upon a circular hole in a two-dimensional conducting sheet

Shegelski¹,

Salayka-Ladouceur²,

Malmgren³

2016

Eur. J. Phys.

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We consider a one-dimensional molecule with a permanent electric dipole moment incident along the line of symmetry of a circular hole in an infinite two-dimensional conducting sheet. We calculate the probabilities of reflection pR and transmission pT of a centre of mass wave packet initially of the form of a Gaussian wave packet and moving toward the hole. We show the dependence of pT and pR on the charge Q of the atoms, the radius a of the hole as compared to the length scale of the bound molecular relative motion state, the mass and energy of the molecule. We compare a fully quantum mechanical treatment to a semiclassical approximation in which the distance between the atoms is constant. Some unexpected and surprising results emerge from this study.

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Tunneling of a diatomic molecule with unbound states in one dimension

Cited by 13 publications

References 18 publications

Quantum tunneling and reflection of a molecule with a single bound state

Quantum tunneling and reflection of a molecule with a single bound state

One Dimensional Time-Dependent Tunnelling of Excitons

Transmission and reflection of a molecule with a dipole moment incident upon a circular hole in a two-dimensional conducting sheet

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