Modeling Atoms, Molecules, and Crystals in One Dimension

spin, hemmer, eigenenergy, eigenstate, schrödinger equation, waves

Solving the time independent Schrödinger equation in one dimension using matrix diagonalisation for five different potentials.

  Solving the Time-Dependent Schrödinger equation

animation, eigenenergy, eigenstate, schrödinger equation, tunneling, scattering, ehrenfest's theorem

The Time-Dependent Schrödinger equation is solved by expressing the solution as a linear combination of (stationary) solutions of the Time-Independent Schrödinger equation.

  One-Dimensional Wave Propagation

animation, schrödinger equation, tunneling, scattering

A one-dimensional wave-packet is propagated forward in time for various different potentials.

  Eigenenergies Through Matrix Diagonalization

harmonic oscillator

The eigenenergies of a system are found by discretizing the Schrödinger equation and finding the eigenvalues of the resulting matrix.

  Numerical Determination of Eigenenergies for an Asymmetric Potential

eigenenergy, forward shooting, eigenstate, schrödinger equation

Using a forward-shooting method to determine the eigenenergies and eigenfunctions of an asymmetric potential in one dimension.

  Hydrogen Molecule Ion

schrödinger equation

Employing Monte Carlo integration to determine the "shape" of the hydrogen molecule ion.

  Band Structures and Newton's Method

schrödinger equation, bloch's theorem, newton's theorem

Using Newton's method to calculate the band structure for the simple Dirac comb potential in one dimension.