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In quantum mechanics the time-independent Schrodinger's equation can be solved for eigenfunctions (also called eigenstates or wave-functions) and corresponding eigenenergies (or energy levels) for a stationary physical system. The wavefunction itself can take on negative and positive values and could be complex.
The square magnitude of the wave-function is the probability density of finding the particle in space at that particular energy level.

3D wavefunctions - Schrodinger's equation

A quantum dot is a physical system that can confine electrons or holes in all three spatial dimensions. The image above shows how stationary wave functions look in box and pyramid-shaped quantum dots. Energy states in rectangular dots are more s-type and p-type in character (i.e., they maintain orbital symmetry). However, in a pyramid-shaped dot the wave functions are mixed due to the asymmetry of the confinement.


Image rendered using nanoHUB tool Quantum Dot Lab (

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Researchers should cite this work as follows:

  • Saumitra Raj Mehrotra; Gerhard Klimeck (2010), "3D wavefunctions,"

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