plot::HOrbital
-- visualize the
electron orbitals of a hydrogen atomplot::HOrbital(
n, l, m)
yields a
visualization of the hydrogen electron orbital with quantum numbers
n
, l
, m
.
plot::HOrbital(n, l, m, Option1, Option2, ...)
n |
- | the principal (energy) quantum number: a positive integer |
l |
- | the angular momentum quantum number: an integer
between 0 and n - 1 |
m |
- | the magnetic quantum number: an integer between
-l and l |
Option1, Option2, ... |
- | options allowed in plot::Surface3d |
an object of type plot::Surface3d
.
plot::HOrbital
.plot::HOrbital
generates a surface of type plot::Surface3d
. It uses the
default settings with one exception: a specialized color scheme is used
to depict information on the radial part of the electron orbit (see
``Background''). Using the Color
option of plot::Surface3d
, this internal color
scheme may be overridden by a user-defined color.plot::HOrbital
may be passed
to the function plot::Scene
to create a graphical scene.
In the call to plot::Scene
, you may specify scene options. Call
plot(...)
to display the scene.
Alternatively, you can pass the surface directly to plot
together with scene options.
The following call yields a symbolic surface object:
>> orbit := plot::HOrbital(3, 2, 0)
plot::Surface3d([cos(phi1) sin(theta1) 2 2 (1.5 cos(theta1) - 0.5) , sin(phi1) sin(theta1) 2 2 (1.5 cos(theta1) - 0.5) , cos(theta1) 2 2 (1.5 cos(theta1) - 0.5) ], theta1 = 0..PI, phi1 = 0..2 PI)
We pass this object to plot
to render the object:
>> plot(orbit, Ticks = None)
With the Grid-Option of plot::Surface3d
, a smoother
surface is generated. The scene option Axis = None
is used
in plot
to switch off the default box around the graphical
scene:
>> orbit := plot::HOrbital(3, 2, 0, Grid = [30, 30], Title = "quantum numbers: 3, 2, 0"): plot(orbit, Axes = None)
The internal coloring is replaced by a new coloring scheme:
>> orbit := plot::HOrbital(3, 2, 0, Grid = [30, 30], Color = [Height]): plot(orbit)
>> delete orbit:
x(r, phi, theta) = r * cos(phi) * sin(theta), y(r, phi, theta) = r * sin(phi) * sin(theta), z(r, phi, theta) = r * cos(theta), r = 0..infinity, phi = 0 .. 2*PI, theta = 0 .. PIthe wave function has the form Psi(x,y,z) = R(r) * Y(phi, theta). The surface is a visualization of the real part of the function Y(phi, theta): the surface is defined by the parameterization
x(phi, theta) = Re(Y(phi, theta))^2 * cos(phi) * sin(theta), y(phi, theta) = Re(Y(phi, theta))^2 * sin(phi) * sin(theta), z(phi, theta) = Re(Y(phi, theta))^2 * cos(theta) .The distance of a surface point to the origin is Re(Y(phi, theta))^2. Hence, the real part of the electron density is reflected by the shape of the surface: the ``bulges'' indicate high probabilities.
The radial part R(r) of the wave function Psi(x,y,z) = R(r) * Y(phi, theta) is only used in the coloring scheme of the surface: high values of R(r)^2 yield bright colors, small values yield dark colors. Red colors indicate points where the real part of the wave function Re(Psi) is positive. Blue colors indicate negative values.
n
are
referred to as a ``shell''. Traditionally, the following shell symbols
are used:
n | 1 2 3 4 ... -------------+------------ shell symbol | K L M N ...The following symbols are associated with the angular momentum:
l | 0 1 2 3 4 5 ... -------+---------------- symbol | s p d f g h ...