2004
DOI: 10.1103/physreve.69.036705
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Eigenvalue problem of the Schrödinger equation via the finite-difference time-domain method

Abstract: We present a very efficient scheme to calculate the eigenvalue problem of the time-independent Schrödinger equation. The eigenvalue problem can be solved via an initial-value procedure of the time-dependent Schrödinger equation. First, the time evolution of the wave function is calculated by the finite-difference time-domain method. Then the eigenenergies of the electron system can be obtained through a fast Fourier transformation along the time axis of the wave function after some point. The computing effort … Show more

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Cited by 14 publications
(5 citation statements)
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“…We begin describing the FDTD implementation of the time-dependent Schrödinger equation [ 13 , 14 ], which is written in the following form …”
Section: The Finite-difference Time-domain Methodsmentioning
confidence: 99%
“…We begin describing the FDTD implementation of the time-dependent Schrödinger equation [ 13 , 14 ], which is written in the following form …”
Section: The Finite-difference Time-domain Methodsmentioning
confidence: 99%
“…The proposed procedures which is based on the BOR-FDTD method and the Wick rotation transformation has several advantages over the traditional 3D-FDTD method [33]. First, due to employing only real-valued wavefunctions rather than dealing with complex wavefunctions and having two coupled Schrödinger equations, the simulation needs less running-time and memory.…”
Section: Q-bor-fdtd Algorithm For Three-dimensional Schrödinger Equationmentioning
confidence: 99%
“…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%
“…An FDTD method for electronic systems has already been proposed [12][13][14], called the FDTD method for quantum device (FDTD-Q). In the FDTD-Q method, electronic wave function is discretized and divided into real and imaginary parts, ψ(r)=ψ R (r)+iψ I (r), and then the Schrödinger equation is solved by temporally and alternately calculating ψ R (t) and ψ I (r), in a similar manner to the FDTD method.…”
Section: Introductionmentioning
confidence: 99%