Search results
Results from the WOW.Com Content Network
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 ...
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 nucleus of a single positively charged proton and a single negatively charged electron bound to the nucleus by the Coulomb force.
The main reason is that its Schrödinger equation is very difficult to solve. Applications are restricted to small systems like the hydrogen molecule. Almost all calculations of molecular wavefunctions are based on the separation of the Coulomb Hamiltonian first devised by Born and Oppenheimer. The nuclear kinetic energy terms are omitted from ...
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.
Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually autonomous and logically consistent formulation of quantum mechanics.
The hydrogen atom or hydrogen-like atom e.g. positronium; The hydrogen atom in a spherical cavity with Dirichlet boundary conditions [4] The Mie potential [5] The Hooke's atom; The Morse potential; The Spherium atom; Zero range interaction in a harmonic trap [6] Multistate Landau–Zener models [7]
From the equations, the power series must start with at least an order of to satisfy the real part of the equation; for a good classical limit starting with the highest power of the Planck constant possible is preferable, which leads to = = and = = (), with the following constraints on the lowest order terms, () = (()) and () =
The Hooke's atom is a simple model of the helium atom using the quantum harmonic oscillator. Modelling phonons, as discussed above. A charge q {\displaystyle q} with mass m {\displaystyle m} in a uniform magnetic field B {\displaystyle \mathbf {B} } is an example of a one-dimensional quantum harmonic oscillator: Landau quantization .