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

Sudiarta, I Wayan; Angraini, Lily Maysari

doi:10.1063/1.5064196

Cited by 6 publications

(4 citation statements)

References 11 publications

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“…Sudiarta dan Geldart [8] menerapkan lagi metode FDTD grid uniform untuk kasus density matrix satu partikel. Sudiarta dan Angraini [9] berhasil mensimulasikan dua elektron yang berintraksi pada potensial quantum dot. Dari beberapa hasil penelitian di atas terbukti bahwa metode FDTD grid uniform dapat digunakan untuk menyelesaikan persamaan diferensial secara sederhana.…”

Section: Pendahuluanunclassified

Metode Numerik FDTD dengan Non-Uniform Grid untuk Solusi Persamaan Schrӧdinger

Yuliani¹,

Sudiarta²

2020

J. Fis. dan Apl.

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Pada paper ini, spasi grid yang non-uniform (tidak seragam) digunakan untuk meningkatkan akurasi pada metode finite difference time domain (FDTD). Pada umumnya, metode FDTD menggunakan grid seragam (uniform) sehingga pada kasus dengan perubahan potensial yang besar membutuhkan spasi grid yang cukup kecil dan jumlah grid yang banyak untuk mendapatkan akurasi yang diinginkan. Dengan spasi grid tidak seragam, posisi titik grid disesuaikan dengan perubahan potensial sehingga akurasi tinggi dapat diperoleh tanpa menambah jumlah grid. Pada paper ini, komparasi hasil metode FDTD dengan grid uniform dan non-uniform untuk sistem partikel di dalam potensial konstan (kotak) dan tidak konstan (osilator harmonik) diberikan. Sesuai ekspektasi, hasil numerik menunjukkan bahwa penurunan akurasi diperoleh dengan menggunakan grid non-uniform untuk kasus potensial konstan, tetapi terjadi peningkatan akurasi untuk kasus potensial tidak konstan.

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Section: Pendahuluanunclassified

Metode Numerik FDTD dengan Non-Uniform Grid untuk Solusi Persamaan Schrӧdinger

Yuliani¹,

Sudiarta²

2020

J. Fis. dan Apl.

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“…The FDTD method [26] is a numerical technique that has been used in several branches of Physics. It has been extensively employed in various applications in electrodynamics, nano-optics, and nanophotonics for solving Maxwell's equations and also in quantum mechanics for solving the Schrödinger equation [27][28][29][30][31][32][33][34][35][36][37]. This kind of the FDTD application has been established by Sullivan et al (2001), and Soriano et al (2004), to study the eigenvalues, eigenstates and dynamics of several quantum nanostructures [35], such as, quantum well wires [34], spin evolution and two electrons in a quantum dot [36,37].…”

Section: Introductionmentioning

confidence: 99%

Q-BOR–FDTD method for solving Schrödinger equation for rotationally symmetric nanostructures with hydrogenic impurity

Firoozi¹,

Mohammadi²,

Khordad³

et al. 2022

Phys. Scr.

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An efficient method inspired by the traditional body of revolution finite-difference time-domain (BOR-FDTD) method is developed to solve the Schrodinger equation for rotationally symmetric problems. As test cases, spherical, cylindrical, cone-like quantum dots, harmonic oscillator, and spherical quantum dot with hydrogenic impurity are investigated to check the efficiency of the proposed method which we coin as Quantum BOR-FDTD (Q-BOR-FDTD) method. The obtained results are analysed and compared to the 3-D FDTD method, and the analytical solutions. Q-BOR-FDTD method proves to be very accurate and time and memory efficient by reducing a three-dimensional problem to a two-dimensional one, therefore one can employ very fine meshes to get very precise results. Moreover, it can be exploited to solve problems including hydrogenic impurities which is not an easy task in the traditional FDTD calculation due to singularity problem. To demonstrate its accuracy, we consider spherical and cone-like core-shell QD with hydrogenic impurity. Comparison with analytical solutions confirms that Q-BOR–FDTD method is very efficient and accurate for solving Schrodinger equation for problems with hydrogenic impurity

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“…A multitude of different implementations exist, depending on the spatial discretization and the time propagation, each having their strengths and weaknesses. Moreover, the FDTD method has also been applied to various related equations such as the non-linear Schrödinger equation [20][21][22][23][24][25][26], the Gross-Pitaevskii equations [27], and the stationary Schrödinger equation by performing a Wick rotation [28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%