Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Propagation of !D Electron wave equations in lattice system

Fahrudin Nugroho

Published May 16, 2009• 0 citations
OpenAlex

Abstract

The propagation of one dimensional electron wave function in periodic potential have been simulated. Gaussian wave function was chose to simulate the wave packet for the electron. The simulation or periodic potential shows that it follows Bloch theorem. Many problems related with the shape of potential are simulated also. Initial energy chose as tested parameter, which correspond to the speed of wave packet and related with the energy of the electron, and its show that for greater energy the spreading of wave packet become slower. The dynamical parameter makes possibilities to evaluate the propagation every time we need.

Related papers

Quantum dynamics of charge transfer on the one-dimensional lattice： Wave packet spreading and recurrence

Лихачев, Shevaleevskii

The wave function temporal evolution on the one-dimensional(1D) lattice is considered in the tight-binding approximation. The lattice consists of N equal sites and one impurity site(donor). The donor differs from other lattice sites by the on-site electron energy E and the intersite coupling C. The moving wave packet is formed from the wave function initially localized on the donor. The exact solution for the wave packet velocity and the shape is derived at different values E and C. The velocity has the maximal possible group velocity v = 2. The wave packet width grows with time ～ t1/3and its amplitude decreases ～ t-1/3. The wave packet reflects multiply from the lattice ends. Analytical expressions for the wave packet front propagation and recurrence are in good agreement with numeric simulations.

中国物理B：英文版•Jan 1, 2016•0 citations

Quantum dynamics of charge transfer on the one-dimensional lattice: Wave packet spreading and recurrence

Vladimir Nikolaevich Likhachev, O. I. Shevaleevskiǐ, George A Vinogradov

The wave function temporal evolution on the one-dimensional (1D) lattice is considered in the tight-binding approximation.The lattice consists of N equal sites and one impurity site (donor).The donor differs from other lattice sites by the on-site electron energy E and the intersite coupling C. The moving wave packet is formed from the wave function initially localized on the donor.The exact solution for the wave packet velocity and the shape is derived at different values E and C. The velocity has the maximal possible group velocity v = 2.The wave packet width grows with time ∼ t 1/3 and its amplitude decreases ∼ t -1/3 .The wave packet reflects multiply from the lattice ends.Analytical expressions for the wave packet front propagation and recurrence are in good agreement with numeric simulations.

Chinese Physics B•Jan 1, 2016•10 citations

Bloch electron in an electric field: a comparison between the exact wave function and the Houston approximation

John N. Churchill, F.E. Holmstrom

The time-evolution of a wave packet in a perfectly periodic lattice potential is considered for an electron that is in a zero-field Bloch energy eigenstate prior to the adiabatic application of a uniform d.c. electric field. Power series expansions in time are constructed for both the exact wave function and the Houston wave function. A comparison of the coefficients in these two expansions shows that the Houston function diverges instantly and drastically from the exact wave function. A special-case example is presented for which the exact wave function is pure-real for all values of time whereas the corresponding Houston function is not.

Physica Scripta•Nov 1, 1994•1 citation

Dynamics of an Electron Wave Packet in a Quantum Dot Subjected to Magnetic Fields

Tsuyoshi Ueta

The time evolution of a Gaussian wave packet of an electron, which is confined in a quantum dot subjected to uniform magnetic fields, is analytically studied in terms of the exact Feynman kernel. The central position of the wave packet follows the classical trajectory. Although the motion of the central position is aperiodic due to its dual period, the variance of the probability density changes periodically. If the shape of the initial wave packet is the same as that of the wave function of the ground state, its shape never alters. For more general systems in which the periodic full revival of electron wave packets is realized, the characteristic of energy eigenvalues is discussed.

Journal of the Physical Society of Japan•Mar 15, 1995•4 citations

A note on the application of the semiclassical wave packet dynamics

Michal Kolář, M. K. Ali, S. F. O’Shea

The optimal choice of the initial parameters of the Gaussian wave packets in the time dependent quantum mechanical calculations using a Gaussian wave packet representation of the wave function is discussed. The proposed procedure is illustrated with the simple case of one dimensional scattering and the propagation of the ground state of the Morse potential.

The Journal of Chemical Physics•Jan 15, 1989•2 citations

Wave Packet Motion in Harmonic Potential

Hideo Tsuru

A motion of a Gaussian wave packet of a single electron in a harmonic potential is obtained by solving the time dependent Schrödinger equation analytically. The analytic formula of the phase of the wave function which depends on both time and space is also presented explicitly. The probability density of the wave packet moves changing its width and central position periodically. The period of the change of the width is half of that of the central position. The interpretation of these periodic changes in terms of the Green's function which can be derived by the path integration formulation is also discussed.

Journal of the Physical Society of Japan•Nov 15, 1991•7 citations
The propagation of one dimensional electron wave function in periodic potential have been simulated. Gaussian wave function was chose to simulate the wave packet for the electron. The simulation or periodic potential shows that it follows Bloch theorem. Many problems related with the shape of potential are simulated also. Initial energy chose as tested parameter, which correspond to the speed of wave packet and related with the energy of the electron, and its show that for greater energy the spreading of wave packet become slower. The dynamical parameter makes possibilities to evaluate the propagation every time we need.
The wave function temporal evolution on the one-dimensional(1D) lattice is considered in the tight-binding approximation. The lattice consists of N equal sites and one impurity site(donor). The donor differs from other lattice sites by the on-site electron energy E and the intersite coupling C. The moving wave packet is formed from the wave function initially localized on the donor. The exact solution for the wave packet velocity and the shape is derived at different values E and C. The velocity has the maximal possible group velocity v = 2. The wave packet width grows with time ～ t1/3and its amplitude decreases ～ t-1/3. The wave packet reflects multiply from the lattice ends. Analytical expressions for the wave packet front propagation and recurrence are in good agreement with numeric simulations.
The wave function temporal evolution on the one-dimensional (1D) lattice is considered in the tight-binding approximation.The lattice consists of N equal sites and one impurity site (donor).The donor differs from other lattice sites by the on-site electron energy E and the intersite coupling C. The moving wave packet is formed from the wave function initially localized on the donor.The exact solution for the wave packet velocity and the shape is derived at different values E and C. The velocity has the maximal possible group velocity v = 2.The wave packet width grows with time ∼ t 1/3 and its amplitude decreases ∼ t -1/3 .The wave packet reflects multiply from the lattice ends.Analytical expressions for the wave packet front propagation and recurrence are in good agreement with numeric simulations.
The time-evolution of a wave packet in a perfectly periodic lattice potential is considered for an electron that is in a zero-field Bloch energy eigenstate prior to the adiabatic application of a uniform d.c. electric field. Power series expansions in time are constructed for both the exact wave function and the Houston wave function. A comparison of the coefficients in these two expansions shows that the Houston function diverges instantly and drastically from the exact wave function. A special-case example is presented for which the exact wave function is pure-real for all values of time whereas the corresponding Houston function is not.
The time evolution of a Gaussian wave packet of an electron, which is confined in a quantum dot subjected to uniform magnetic fields, is analytically studied in terms of the exact Feynman kernel. The central position of the wave packet follows the classical trajectory. Although the motion of the central position is aperiodic due to its dual period, the variance of the probability density changes periodically. If the shape of the initial wave packet is the same as that of the wave function of the ground state, its shape never alters. For more general systems in which the periodic full revival of electron wave packets is realized, the characteristic of energy eigenvalues is discussed.
A motion of a Gaussian wave packet of a single electron in a harmonic potential is obtained by solving the time dependent Schrödinger equation analytically. The analytic formula of the phase of the wave function which depends on both time and space is also presented explicitly. The probability density of the wave packet moves changing its width and central position periodically. The period of the change of the width is half of that of the central position. The interpretation of these periodic changes in terms of the Green's function which can be derived by the path integration formulation is also discussed.