Demos.FreeParticle.Main

WavePacket demo example: Free particle

Any solution of the Schrödinger equation for a free particle (vanishing potential energy) can be regarded as a superposition of (infinitely extended) plane waves. These wavefunctions are characterized by wavenumber vectors K which are related to the quantum mechanical momentum operator P through the famous de Broglie's relation P = ħ K which is at the heart of the wave-particle dualism in quantum physics. Localized wavepackets can be created by specific superpositions of plane waves.

Gaussian wavepacket in one dimension

For the special case of a Gaussian distribution of wavenumbers (momenta), one obtains a localized, Gaussian-shaped wavefunction in position space representation, too. This is due to the properties of the Fourier transformation connecting position and momentum space representation of wavefunctions. Learn more

Gaussian wavepacket in two dimensions

In higher dimensionality, the physics of free particles remains essentially unchanged. The case of vanishing potential represents a (trivial) example of separable potentials where the multi-dimensional wavefunctions can be written as products of one-dimensional wavefunctions. Learn more

"Schrödinger Cat" states

The celebrated "Schrödinger Cat" state is a much discussed example for the apparent paradoxa of quantum mechanics. A simple yet elegant way to represent it in terms of wavefunctions in position space is a coherent superposition of two Gaussian wavepackets. Its characteristic properties are revealed in phase space (Wigner) representation. Learn more