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Quantum Mechanics: Wavepackets

By Dragica Vasileska1, Gerhard Klimeck2

1. Arizona State University 2. Purdue University

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In physics, a wave packet is an envelope or packet containing an arbitrary number of wave forms. In quantum mechanics the wave packet is ascribed a special significance: it is interpreted to be a "probability wave" describing the probability that a particle or particles in a particular state will be measured to have a given position and momentum.

By applying the Schrödinger equation in quantum mechanics it is possible to deduce the time evolution of a system, similar to the process of the Hamiltonian formalism in classical mechanics. The wave packet is a mathematical solution to the Schrödinger equation. The square of the area under the wave packet solution is interpreted to be the probability density of finding the particle in a region.

In the coordinate representation of the wave (such as the Cartesian coordinate system) the position of the wave is given by the position of the packet. Moreover, the narrower the spatial wave packet, and therefore the better defined the position of the wave packet, the larger the spread in the momentum of the wave. This trade-off between spread in position and spread in momentum is one example of the Heisenberg uncertainty principle.

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    Researchers should cite this work as follows:

    • Dragica Vasileska; Gerhard Klimeck (2008), "Quantum Mechanics: Wavepackets,"

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    In This Series

    1. Reading Material: Wavepackets

      07 Jul 2008 | Teaching Materials | Contributor(s): Dragica Vasileska

    2. Homework Assignment: Wavepackets

      07 Jul 2008 | Teaching Materials | Contributor(s): Dragica Vasileska, Gerhard Klimeck, a resource for nanoscience and nanotechnology, is supported by the National Science Foundation and other funding agencies. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.