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Are electron orbitals spherical harmonics? Edit: orbitals

by mmastrac 5y ago

aaaaaaaaaaab 5y ago
Yes.
- gus_massa 5y ago
  More details: The orbitals are the product of an Harmonic Orbital and a radial function. More details in https://en.wikipedia.org/wiki/Atomic_orbital#Types_of_orbitals https://en.wikipedia.org/wiki/Atomic_orbital#Types_of_orbita... and https://en.wikipedia.org/wiki/Hydrogen-like_atom#Non-relativistic_wavefunction_and_energy https://en.wikipedia.org/wiki/Hydrogen-like_atom#Non-relativ... Note that this is the initial selection of orbitals. The "real"[1] orbitals are linear combinations of them. In some cases it's good enough to mix them using some easy combinations like in https://en.wikipedia.org/wiki/Orbital_hybridisation https://en.wikipedia.org/wiki/Orbital_hybridisation but in the general cases you must use a computer to calculate the best combination https://en.wikipedia.org/wiki/Hartree%E2%80%93Fock_method https://en.wikipedia.org/wiki/Hartree%E2%80%93Fock_method . [1] It get's more complicated.
deleted 5y ago
[deleted]
frutiger 5y ago
Electrons do not orbit. For the simple case of an electron in a hydrogen atom, energy-stable wavefunctions are products of three separate functions: exponential function, a laguerre polynomial function and a spherical harmonic.
- Sharlin 5y ago
  Presumably the GP meant orbitals.
  - robotsteve2 5y ago
    It's an important distinction. A lot of people would like to think electrons orbit the nucleus like planets orbit a star.
    - Sharlin 5y ago
      Yes, but someone thinking in terms of the Bohr model would not ask is the orbits are (described by) spherical harmonics.
dr_dshiv 5y ago
How might spherical harmonics be relevant for quantum computing? I’m on the hunt for visualizations. (Not to be confused with the Bloch Sphere!)
- robotsteve2 5y ago
  Spherical harmonics are a useful mathematical basis set for eigenfunctions of a Schrodinger equation describing a hydrogen atom like system. There's nothing particularly special about them, and they fail to be a good basis set for solutions of other types of quantum systems. Conversely, they can be useful for non-quantum systems - any sort of wave equation in a sphere. It's not an intrinsically quantum mechanical thing.
  - dr_dshiv 5y ago
    Idk… seems intrinsic in so far as waves are intrinsic to Quantum Mechanics. Check out these visuals from “the orbitron”: https://winter.group.shef.ac.uk/orbitron/ https://winter.group.shef.ac.uk/orbitron/

Are electron orbitals spherical harmonics? Edit: orbitals

aaaaaaaaaaab 5y ago

Yes.

gus_massa 5y ago
More details: The orbitals are the product of an Harmonic Orbital and a radial function. More details in https://en.wikipedia.org/wiki/Atomic_orbital#Types_of_orbitals https://en.wikipedia.org/wiki/Atomic_orbital#Types_of_orbita... and https://en.wikipedia.org/wiki/Hydrogen-like_atom#Non-relativistic_wavefunction_and_energy https://en.wikipedia.org/wiki/Hydrogen-like_atom#Non-relativ... Note that this is the initial selection of orbitals. The "real"[1] orbitals are linear combinations of them. In some cases it's good enough to mix them using some easy combinations like in https://en.wikipedia.org/wiki/Orbital_hybridisation https://en.wikipedia.org/wiki/Orbital_hybridisation but in the general cases you must use a computer to calculate the best combination https://en.wikipedia.org/wiki/Hartree%E2%80%93Fock_method https://en.wikipedia.org/wiki/Hartree%E2%80%93Fock_method . [1] It get's more complicated.

deleted 5y ago

[deleted]

frutiger 5y ago

Electrons do not orbit. For the simple case of an electron in a hydrogen atom, energy-stable wavefunctions are products of three separate functions: exponential function, a laguerre polynomial function and a spherical harmonic.

Sharlin 5y ago
Presumably the GP meant orbitals.
- robotsteve2 5y ago
  It's an important distinction. A lot of people would like to think electrons orbit the nucleus like planets orbit a star.
  - Sharlin 5y ago
    Yes, but someone thinking in terms of the Bohr model would not ask is the orbits are (described by) spherical harmonics.

dr_dshiv 5y ago

How might spherical harmonics be relevant for quantum computing? I’m on the hunt for visualizations. (Not to be confused with the Bloch Sphere!)

robotsteve2 5y ago
Spherical harmonics are a useful mathematical basis set for eigenfunctions of a Schrodinger equation describing a hydrogen atom like system. There's nothing particularly special about them, and they fail to be a good basis set for solutions of other types of quantum systems. Conversely, they can be useful for non-quantum systems - any sort of wave equation in a sphere. It's not an intrinsically quantum mechanical thing.
- dr_dshiv 5y ago
  Idk… seems intrinsic in so far as waves are intrinsic to Quantum Mechanics. Check out these visuals from “the orbitron”: https://winter.group.shef.ac.uk/orbitron/ https://winter.group.shef.ac.uk/orbitron/