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A hydrogen atom is an atom of the chemical element hydrogen. ... or the generalized Laguerre polynomial appearing in the hydrogen wave function is + ...
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 ...
A wave function can be an eigenvector of an observable, ... The Schrödinger equation for a hydrogen atom can be solved by separation of variables. [24]
The non-relativistic Schrödinger equation and relativistic Dirac equation for the hydrogen atom can be solved analytically, owing to the simplicity of the two-particle physical system. The one-electron wave function solutions are referred to as hydrogen-like atomic orbitals. Hydrogen-like atoms are of importance because their corresponding ...
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).
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.
This procedure is analogous to the separation performed in the hydrogen-like atom problem, but with a different spherically symmetric potential =, where μ is the mass of the particle. Because m will be used below for the magnetic quantum number, mass is indicated by μ , instead of m , as earlier in this article.
The wave function of the ground state of a hydrogen atom is a spherically symmetric distribution centred on the nucleus, which is largest at the center and reduces exponentially at larger distances. The electron is most likely to be found at a distance from the nucleus equal to the Bohr radius. This function is known as the 1s atomic orbital.