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Depiction of a hydrogen atom showing the diameter as about twice the Bohr model radius. (Image not to scale) A hydrogen atom is an atom of the chemical element hydrogen.The electrically neutral hydrogen atom contains a single positively charged proton in the nucleus, and a single negatively charged electron bound to the nucleus by the Coulomb force.
The displayed functions are solutions to the Schrödinger equation. Obviously, not every function in L 2 satisfies the Schrödinger equation for the hydrogen atom. The function space is thus a subspace of L 2. The displayed functions form part of a basis for the function space. To each triple (n, ℓ, m), there corresponds a basis wave function ...
Below, a number of drum membrane vibration modes and the respective wave functions of the hydrogen atom are shown. A correspondence can be considered where the wave functions of a vibrating drum head are for a two-coordinate system ψ(r, θ) and the wave functions for a vibrating sphere are three-coordinate ψ(r, θ, φ).
The Schrödinger equation for the electron in a hydrogen atom (or a hydrogen-like atom) is = where is the electron charge, is the position of the electron relative to the nucleus, = | | is the magnitude of the relative position, the potential term is due to the Coulomb interaction, wherein is the permittivity of free space and = + is the 2-body ...
As is known from the analytic solutions for the hydrogen atom, the eigenfunctions of the angular part of the wave function are spherical harmonics. However, the solutions of the non-relativistic Schrödinger equation without magnetic terms can be made real.
In the end, the model was replaced by the modern quantum-mechanical treatment of the hydrogen atom, which was first given by Wolfgang Pauli in 1925, using Heisenberg's matrix mechanics. The current picture of the hydrogen atom is based on the atomic orbitals of wave mechanics, which Erwin Schrödinger developed in 1926.
For example, the electron wave function for an unexcited hydrogen atom is a spherically symmetric function known as an s orbital . Analytic solutions of the Schrödinger equation are known for very few relatively simple model Hamiltonians including the quantum harmonic oscillator , the particle in a box , the dihydrogen cation , and the ...
A wave function for a single electron on 5d atomic orbital of a hydrogen atom. The solid body shows the places where the electron's probability density is above a certain value (here 0.02 nm −3): this is calculated from the probability amplitude. The hue on the colored surface shows the complex phase of the wave function.