Search results
Results from the WOW.Com Content Network
As such, the equation cannot be applied to the description of atoms, since the electron is a spin 1 / 2 particle. In the non-relativistic limit the equation reduces to the Schrödinger equation for a spinless charged particle in an electromagnetic field: [18]
In theoretical physics, the Madelung equations, or the equations of quantum hydrodynamics, are Erwin Madelung's alternative formulation of the Schrödinger equation for a spinless non relativistic particle, written in terms of hydrodynamical variables, similar to the Navier–Stokes equations of fluid dynamics. [1]
Relativistic quantum chemistry combines relativistic mechanics with quantum chemistry to calculate elemental properties and structure, especially for the heavier elements of the periodic table. A prominent example is an explanation for the color of gold : due to relativistic effects, it is not silvery like most other metals.
A free particle with mass in non-relativistic quantum mechanics is described by the free Schrödinger equation: (,) = (,) where ψ is the wavefunction of the particle at position r and time t . The solution for a particle with momentum p or wave vector k , at angular frequency ω or energy E , is given by a complex plane wave :
In quantum mechanics, the particle in a box model (also known as the infinite potential well or the infinite square well) describes the movement of a free particle in a small space surrounded by impenetrable barriers. The model is mainly used as a hypothetical example to illustrate the differences between classical and quantum systems. In ...
When quantum mechanics was originally formulated, it was applied to models whose correspondence limit was non-relativistic classical mechanics. For instance, the well-known model of the quantum harmonic oscillator uses an explicitly non-relativistic expression for the kinetic energy of the oscillator, and is thus a quantum version of the ...
A model of the atomic nucleus showing it as a compact bundle of the two types of nucleons: protons (red) and neutrons (blue). As a first approximation, the nucleus can be treated as composed of non-interacting proton and neutron gases. The three-dimensional isotropic and non-relativistic uniform Fermi gas case is known as the Fermi sphere.
In Cartesian coordinates, the Lagrangian of a non-relativistic classical particle in an electromagnetic field is (in SI Units): = ˙ + ˙ where q is the electric charge of the particle, φ is the electric scalar potential, and the A i, i = 1, 2, 3, are the components of the magnetic vector potential that may all explicitly depend on and .