Quantum Mechanics Wave Function in 3D

In summary, the conversation discusses plotting a wave function in 3 dimensions and the use of complex values. It is noted that while we usually refer to 3 dimensions, the wave function can technically be considered as existing in four dimensions. Suggestions for visualizing the wave function are also mentioned, such as using a density plot or plots of orbitals with a certain probability threshold. Examples of these types of plots can be found in the Wikipedia article for the hydrogen atom.
  • #1
Icycub
12
1
I was wondering if it's possible to plot a wave function that is a function of 3 coordinates, such as (x, y, z). The text my class uses calls this Quantum Mechanics in 3 dimensions, but wouldn't this technically by four dimensions?
 
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  • #2
The wave function itself is complex valued, so that's 2 values (real and imaginary values) at each position (x,y,z).

We usually say 3 dimensions, because we mean 3 space dimensions.
 
  • #3
What makes more sense is to visualize ##|\psi(\vec{x})|^2##. For a qualitative overview a density plot is nice. Another way are plots of "orbitals", i.e., the places with a probability >some value. See, e.g., the figures in the Wikipedia article for the hydrogen atom in the English and German Wikipedia:

https://en.wikipedia.org/wiki/Hydrogen_atom
https://de.wikipedia.org/wiki/Wasserstoffatom
 
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1. What is the wave function in 3D quantum mechanics?

The wave function in 3D quantum mechanics is a mathematical representation of the state of a quantum system. It describes the probability of finding a particle at a certain position in space and time.

2. How is the wave function related to the Schrödinger equation?

The wave function is a solution to the Schrödinger equation, which is a fundamental equation in quantum mechanics that describes the time evolution of a quantum system. The wave function is used to calculate the energy and other properties of the system.

3. Can the wave function be used to predict the exact position of a particle?

No, the wave function only describes the probability of finding a particle at a certain position. According to the principles of quantum mechanics, the exact position of a particle cannot be known with certainty.

4. What is the significance of the wave function collapsing?

The collapse of the wave function is a fundamental concept in quantum mechanics. It refers to the sudden change in the state of a quantum system when it is observed or measured. This collapse is a result of the interaction between the system and the measurement apparatus.

5. How does the wave function in 3D differ from the wave function in 1D or 2D?

The wave function in 3D takes into account the position of a particle in three-dimensional space, whereas the wave function in 1D or 2D only considers one or two dimensions, respectively. This allows for a more accurate description of the behavior of particles in three-dimensional systems.

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