Determination of excited states of quantum systems by finite difference time domain method (FDTD) with supersymmetric quantum mechanics (SUSY-QM)

Sudiarta, I Wayan; Angraini, Lily Maysari

doi:10.1063/1.4946933

Cited by 2 publications

(2 citation statements)

References 7 publications

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“…To solve the time-independence Schrödinger equation, the FDTD method can be devided into two methods: realtime FDTD (R-FDTD) method [3,5] and imaginary-time FDTD (I-FDTD) method [6,7,8,9]. The R-FDTD method uses evolution of a wavefunction by the discretized time-dependence Schrödinger equation and Fourier transformation procedure to obtain eigen energies and wavefunctions.…”

Section: Introductionmentioning

confidence: 99%

The finite difference time domain (FDTD) method to determine energies and wave functions of two-electron quantum dot

Sudiarta¹,

Angraini²

2018

AIP Conference Proceedings

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The finite difference time domain (FDTD) method has been successfully applied to obtain energies and wave functions for two electrons in a quantum dot modeled by a three dimensional harmonic potential. The FDTD method uses the time-dependent Schrdinger equation (TDSE) in imaginary time. The TDSE is numerically solved with an initial random wave function and after enough simulation time, the wave function converges to the ground state wave function. The excited states are determined by using the same procedure for the ground state with additional constraints that the wave function must be orthogonal with all lower energy wave functions. The numerical results for energies and wave functions for different parameters of confinement potentials are given and compared with published results using other numerical methods. It is shown that the FDTD method gives accurate energies and wave functions.

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Section: Introductionmentioning

confidence: 99%

The finite difference time domain (FDTD) method to determine energies and wave functions of two-electron quantum dot

Sudiarta¹,

Angraini²

2018

AIP Conference Proceedings

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“…Sudiarta and Geldart (2007) have used the FDTD method to compute the single density matrix particle. Sudiarta and Angraini (2016) have also applied the FDTD method with the symmetry quantum mechanics to obtain the ground and the excited state of particle in one dimensional (1D) potential. The FDTD method have been also used by Sudiarta and Angraini (2018) to determine energies and wave functions of two -electron quantum dots that was modeled by three dimensional (3D) oscillator harmonic potential.…”

Section: Introductionmentioning

confidence: 99%

Non-Standard and Numerov Finite Difference Schemes for Finite Difference Time Domain Method to Solve One- Dimensional Schrödinger Equation

Angraini

Sudiarta

2018

J. Phys.: Theor. Appl.

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The purpose of this paper is to show some improvements of the finite-difference time domain (FDTD) method using Numerov and non-standard finite difference (NSFD) schemes for solving the one-dimensional Schrödinger equation. Starting with results of the unmodified FDTD method, Numerov-FD and NSFD are applied iteratively to produce more accurate results for eigen energies and wavefunctios. Three potential wells, infinite square well, harmonic oscillator and Poschl-Teller, are used to compare results of FDTD calculations. Significant improvements in the results for the infinite square potential and the harmonic oscillator potential are found using Numerov-NSFD scheme, and for Poschl-Teller potential are found using Numerov scheme.

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Determination of excited states of quantum systems by finite difference time domain method (FDTD) with supersymmetric quantum mechanics (SUSY-QM)

Cited by 2 publications

References 7 publications

The finite difference time domain (FDTD) method to determine energies and wave functions of two-electron quantum dot

The finite difference time domain (FDTD) method to determine energies and wave functions of two-electron quantum dot

Non-Standard and Numerov Finite Difference Schemes for Finite Difference Time Domain Method to Solve One- Dimensional Schrödinger Equation

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