Bound-state eigenvalues of the square-well potential

Murphy, R. D.; Phillips, Julia M.

doi:10.1119/1.10381

Cited by 15 publications

(14 citation statements)

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“…The result of energy Eigen values for these boundary condition parameters using the iteration method are tabulated in Table (3). The results of table (3) show that the following remarks:…”

Section: -2 Potential Depth (Pd) Effectmentioning

confidence: 69%

Section: Introductionmentioning

confidence: 99%

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Solving Schrödinger Equation for Finite Potential Well Using the Iterative Method

Al-Ani

Abid

2019

ANJS

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The quantum Finite Square Well (FSW) model is a well-known topic in most quantum mechanics (QM) books. A couple of equations can be derived from one dimensional Schrodinger equation for a finite potential well for describing the bound Eigen states within the well. Sometimes the FSW problem does not have an exact solution, yet, there are in fact exact solutions.In this work a computational techniques is adopted to find the exact solution for FSW. To achieve this computational solution, a computer program has been written in Basic language for calculating the Eigen state energy for a particle confined in finite potential well using the iterative method (IM). Six values of potential width have been studied with potential depth. The results showed that wider potential width led us to more bound states, while narrower potential width led us to less bound states. Six values of potential depth have been studied with potential width. The results showed that larger potential depth led us to more bound states, while smaller potential width led us to less bound states.A Comparison Between Finite and Infinite Potential Well has been also presented. The result of comparison showed that energy levels of an infinite well are much higher than that the corresponding energy levels for finite potential well.In general, the matching between the results of the iterative method and the graphical method (GM) proving that the iteration method can be regarded as a useful tool for describing the solutions of the 1-dimensional FSW problem.

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“…The result of energy Eigen values for these boundary condition parameters using the iteration method are tabulated in Table (3). The results of table (3) show that the following remarks:…”

Section: -2 Potential Depth (Pd) Effectmentioning

confidence: 69%

Section: Introductionmentioning

confidence: 99%

Solving Schrödinger Equation for Finite Potential Well Using the Iterative Method

Al-Ani

Abid

2019

ANJS

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“…In the well, electrons can only occupy discrete energy levels, (see for instance Murphy and Phillips [8]). When the device is biased current flows through the device by several different mechanisms.…”

Section: Discussion Of the Current Voltage Relationmentioning

confidence: 99%

A Millimeter Wave Quantum Well Diode Oscillator

Grönqvist

Rydberg

Hjelmgren

et al. 1988

1988 18th European Microwave Conference

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Experimental results concerning both the DC characteristics and the performance of Quantum Well (QW) diodes as oscillators are given. Two diodes have been manufactured and used in the work where the main difference between them is the doping profile outside the double barrier structure. I-V curves are presented to demonstrate the importance of these design parameters.Also presented are state of the art results for QW oscillators: 84 LW at 77 K and 60 jW at room temperature for a 90 GHz oscillator and 1 ,uW at 176 GHz also at room temperature.INTRODUCTION.

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“…The eigenvalue equations in this form and their graphical representation have been the focus of previous work. 3,5,6 Equation ͑12͒ is equivalent to Eq. ͑10͒, but Eq.…”

Section: Exact and Approximate Energies Of The Finite Square Wellmentioning

confidence: 99%

“…The classic example is the infinite square well, but it is obviously artificial. In the more realistic case where the potential well is finite, the allowed energies as functions of the barrier height can be found by numerically solving a transcendental equation, 3 by graphical methods, [4][5][6][7] or by various approximation techniques. [8][9][10][11][12] The finite quantum well is of great practical importance because it forms the basis for understanding low-dimensional structures such as quantum well devices.…”

Section: Introductionmentioning

confidence: 99%

Exact and approximate energy spectrum for the finite square well and related potentials

Bonfim

Griffiths

2006

American Journal of Physics

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We investigate the problem of a quantum particle in a one-dimensional finite square well. In the standard approach the allowed energies are determined implicitly as the solutions to a transcendental equation. We obtain the spectrum analytically as the solution to a pair of parametric equations and algebraically using a remarkably accurate approximation to the cosine function. The approach is also applied to a variety of other quantum wells.

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Bound-state eigenvalues of the square-well potential

Cited by 15 publications

References 0 publications

Solving Schrödinger Equation for Finite Potential Well Using the Iterative Method

Solving Schrödinger Equation for Finite Potential Well Using the Iterative Method

A Millimeter Wave Quantum Well Diode Oscillator

Exact and approximate energy spectrum for the finite square well and related potentials

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