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File:Hydrogen eigenstate n4 l3 m1.png

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Summary

Description
English: Calculated 4f1 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 orbital is aligned around the z-axis, but remains an eigenfunction if rotated to any direction.

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 = 4: Energy:
  • l = 3: Angular momentum:
  • m = 1: Angular momentum in z-direction:

Since l=3, this is called a f-orbital.

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
Other versions File:Atomic-orbital-cloud n4 l3 m1.png

Properties

Scale Surface probability density Probability inside the solid shape
23px / a0 2.55·10-5 / a03 44.9%

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August 2010

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Date/TimeThumbnailDimensionsUserComment
current00:52, 26 August 2010Thumbnail for version as of 00:52, 26 August 20102,560 × 2,560 (592 KB)Geek3selfmade

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