Hydrogen Atom 1s

 


A 3D plot displays the 1s orbital of a hydrogen atom, illustrating the probability density distribution in a spherical shape. The graph features labeled axes, depicting the spatial dimensions of the orbital.

                                                                     

                                      Hydrogen Atom: 3d Orbital (n=3, l=2, m=2)
                                        
                                            Output image




Here is 3D visualization of all five possible 3d orbitals corresponding to different magnetic quantum numbers (m=−2,−1,0,1,2m = -2, -1, 0, 1, 2).


Each subplot represents a distinct 3d orbital shape, determined by its magnetic quantum number (mm):

  • m=0m = 0: The "classic" dz² orbital, resembling a dumbbell with a toroidal ring.

  • m=±1m = \pm 1: The dxz and dyz orbitals, which have four lobes lying between the coordinate axes.

  • m=±2m = \pm 2: The dxy and dx²-y² orbitals, oriented along the axes.


Key Insights from 3d Orbitals:

  1. All 3d orbitals share the same energy in a hydrogen atom (degenerate energy levels).

  2. The different shapes come from the phase and angular momentum components.

  3. These orbitals are crucial for understanding:

    • Transition metals (since their valence electrons occupy d orbitals).

    • Magnetism (unpaired d-electrons determine magnetic properties).

    • Catalysis (d-orbital interactions enable important chemical reactions).

                                            
                                                                     




Quantum Spin Network Representation of a Hydrogen Atom

The visualization represents the structure of a hydrogen atom using a spin network, where:

  • Nodes represent different quantum states (orbitals, energy levels).

  • Edges represent allowed quantum transitions between states.




Key Observations:

  1. Quantum Energy Levels and Orbital Structure

    • The 1s, 2s, and 2p orbitals are represented as nodes, following hydrogen’s quantum structure.

    • Higher energy levels (nn) exhibit larger values of OO and II, correlating with classical quantum numbers.

  2. Spin Network Encodes Quantum Transitions

    • Edges connect nearby quantum states, representing allowed transitions between energy levels.

    • This structure reflects how electrons jump between states, emitting or absorbing photons.  



                                                                   

Implications for Quantum Mechanics and Quantum Gravity

  1. Emergent Geometry from Quantum Interactions

    • The hydrogen atom’s structure emerges from quantum entanglement patterns in the spin network.

    • Similar to spacetime emergence in quantum gravity models.

  2. Quantum Information Encoding in Atomic Structure

    • Hydrogen’s quantum spin network structure may resemble black hole microstates.

    • Supports holographic descriptions of quantum matter.

  3. Generalizing to Multi-Electron Atoms

    • Larger spin networks could represent heavier atoms, with entanglement encoding electron-electron interactions.



















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