Equations for the transfer matrix elements of the one-dimensional Schr�dinger equation

Chuprikov, N. L.

doi:10.1007/bf00559450

Cited by 7 publications

(18 citation statements)

References 3 publications

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“…In connection with the subsequent analysis of the generalized Hartman paradox, a standard quantum mechanical description of tunneling will be presented by the example of scattering a quantum particle on a one-dimensional system of two identical rectangular potential barriers (when the gap between barriers is zero, this model describes the tunneling of a particle through a single rectangular potential barrier). In doing so, we will use our version [18] of the transfer matrix approach.…”

Section: Standard Model Of Scattering a Particle On A System Of Two I...mentioning

confidence: 99%

“…According to [18], for any semitransparent potential barrier located in the interval [a, b], the elements q and p of the transfer matrix Y (see (2)) can be presented in the form…”

Section: Standard Model Of Scattering a Particle On A System Of Two I...mentioning

confidence: 99%

“…where (see [18]) the transmission coefficient T (a,b) and phases J (a,b) and F (a,b) are determined either by explicit analytical expressions (e.g., for the rectangular barrier and the δ-potential) or by the recurrence relations (for many-barrier structures); R (a,b) = 1 − T (a,b) ; for any symmetric system of barriers, when…”

Section: Standard Model Of Scattering a Particle On A System Of Two I...mentioning

confidence: 99%

“…The 'two-barrier' parameters T two , J two and F two are determined by Eq. ( 8) (see also the recurrence relations for the scattering parameters in [18]):…”

Section: Standard Model Of Scattering a Particle On A System Of Two I...mentioning

confidence: 99%

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Tunneling time and superposition principle

Chuprikov

2017

Preprint

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We show that scattering a quantum particle on a one-dimensional potential barrier as well as scattering the electromagnetic wave on a quasi-one-dimensional layered structure (both represent scattering problems with one 'source' and two 'sinks') violate the superposition principle; the role of nonlinear elements is played here by the potential barrier and the layered structure, splitting the incident (probability and electromagnetic) wave into two parts (transmitted and reflected). This explains why all attempts to solve the tunneling time problem within the framework of the standard (linear) models of these processes, both in quantum mechanics and in classical electrodynamics, have been unsuccessful. We revise the traditional formulation of the superposition principle, present a new (nonlinear) wave model, by the example of the quantum-mechanical scattering process, and show that concepts of the tunneling time developed on its basis are free from the Hartman paradox.

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Section: Standard Model Of Scattering a Particle On A System Of Two I...mentioning

confidence: 99%

“…According to [18], for any semitransparent potential barrier located in the interval [a, b], the elements q and p of the transfer matrix Y (see (2)) can be presented in the form…”

Section: Standard Model Of Scattering a Particle On A System Of Two I...mentioning

confidence: 99%

Section: Standard Model Of Scattering a Particle On A System Of Two I...mentioning

confidence: 99%

“…The 'two-barrier' parameters T two , J two and F two are determined by Eq. ( 8) (see also the recurrence relations for the scattering parameters in [18]):…”

Section: Standard Model Of Scattering a Particle On A System Of Two I...mentioning

confidence: 99%

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Tunneling time and superposition principle

Chuprikov

2017

Preprint

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“…Once the coefficients have been found, the determination of the Ψ E (x; E) in the barrier regions should present no principal problems. In the general case for this purpose one can use, for example, the numerical technique [12].…”

Section: Functional Equation For Wave Functions In the Transfer Matrimentioning

confidence: 99%

Stationary states of an electron in periodic structures in a constant uniform electrical field

Chuprikov

1998

J. Phys.: Condens. Matter

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On the basis of the transfer matrix technique an analytical method to investigate the stationary states, for an electron in one-dimensional periodic structures in an external electrical field, displaying the symmetry of the problem is developed. These solutions are shown to be current-carrying. It is also shown that the electron spectrum for infinite structures is continuous, and the corresponding wave functions do not satisfy the symmetry condition of the problem.

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The role of the spatial dependence of the electron effective mass in forming the Wannier-Stark spectrum

Chuprikov

1999

J. Phys.: Condens. Matter

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We have shown that in the effective mass approach the spatial dependence of the effective mass significantly influences electron properties in the Wannier-Stark problem. That is, if the effective mass of an electron in the infinite periodic structure is uniform everywhere, then its inherent energy spectrum is continuous. But if the effective mass in the adjacent layers of the periodic structure is different, then the energy spectrum must be discrete and consist of so-called Wannier-Stark ladders. To calculate the Wannier-Stark spectrum and the corresponding wave-functions, we proposed a formalism based on the transfer-matrix method. The formalism is used to investigate anticrossing of the levels of the different Wannier-Stark ladders.

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Equations for the transfer matrix elements of the one-dimensional Schr�dinger equation

Cited by 7 publications

References 3 publications

Tunneling time and superposition principle

Tunneling time and superposition principle

Stationary states of an electron in periodic structures in a constant uniform electrical field

The role of the spatial dependence of the electron effective mass in forming the Wannier-Stark spectrum

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