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A quantum number beginning in n = 3,ℓ = 0, describes an electron in the s orbital of the third electron shell of an atom. In chemistry, this quantum number is very important, since it specifies the shape of an atomic orbital and strongly influences chemical bonds and bond angles. The azimuthal quantum number can also denote the number of ...
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]
One particle: N particles: One dimension ^ = ^ + = + ^ = = ^ + (,,) = = + (,,) where the position of particle n is x n. = + = = +. (,) = /.There is a further restriction — the solution must not grow at infinity, so that it has either a finite L 2-norm (if it is a bound state) or a slowly diverging norm (if it is part of a continuum): [1] ‖ ‖ = | |.
is the number operator. When acting on a quantum mechanical photon number state, it returns the number of photons in mode (k, μ). This also holds when the number of photons in this mode is zero, then the number operator returns zero. To show the action of the number operator on a one-photon ket, we consider
The quantum hydrodynamic equation is an equation in Bohmian mechanics, which, it turns out, has a mathematical relationship to classical fluid dynamics (see Madelung equations). Some common experimental applications of these studies are in liquid helium ( 3 He and 4 He ), and of the interior of neutron stars and the quark–gluon plasma .
In quantum mechanics, dynamical pictures (or representations) are the multiple equivalent ways to mathematically formulate the dynamics of a quantum system.. The two most important ones are the Heisenberg picture and the Schrödinger picture.
Quantum turbulence [1] [2] is the name given to the turbulent flow – the chaotic motion of a fluid at high flow rates – of quantum fluids, such as superfluids. The idea that a form of turbulence might be possible in a superfluid via the quantized vortex lines was first suggested by Richard Feynman .
Quantum state tomography is a process by which, given a set of data representing the results of quantum measurements, a quantum state consistent with those measurement results is computed. [50] It is named by analogy with tomography , the reconstruction of three-dimensional images from slices taken through them, as in a CT scan .