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File:Hydrogen eigenstate n5 l2 m1.png

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Summary

Description
English: Calculated 5d1 orbital of an electron's eigenstate in the Coulomb-field of a hydrogen nucleus. An eigenstate is a state which keeps it's shape except for a complex phase when the Hamilton operator is applied, thus being invariant in time while obeying the Schrödinger equation.

The wavefunction is:

The state is an eigenstate of H, L² and Lz, which constitute a complete set of commuting observables.
The quantum numbers mean that the following quantities have a sharp certain value:

  • n = 5: Energy:
  • l = 2: Angular momentum:
  • m = 1: Angular momentum in z-direction:

Since l=2, this is called a d-orbital. The orbital is aligned around the z-axis, but remains an eigenfunction of H and L² if rotated to any direction.

The depicted rigid body is where the probability density exceeds a certain value. The color shows the complex phase of the wavefunction, where blue means real positive, red means imaginary positive, yellow means real negative and green means imaginary negative. The image is raytraced using modified Phong lighting.

The fine structure is neglected.
Date
Source

Own work;

created with hydrogen 1.0
Author Geek3

Properties

Scale Surface probability density Probability inside the solid shape
14px / a0 2.83·10-6 / a03 54.2%

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August 2010

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Date/TimeThumbnailDimensionsUserComment
current21:17, 26 August 2010Thumbnail for version as of 21:17, 26 August 20102,560 × 2,560 (869 KB)Geek3selfmade

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