Quantum models Quantum models A hydrogen atom is an atom of the element hydrogen. It is composed of a single negatively-charged electron, attending a positively-charged proton which is the nucleus of the hydrogen atom. The electron is bound to the proton by the Coulomb force. ...more on Wikipedia about "Hydrogen atom"
In quantum mechanics, when talking about solid materials, the discussion is mainly about crystals - periodic lattices. Here we will discuss a 1-dimensional lattice of positive ions. The one-dimensional particle lattice is a simplified version of the 3D infinite potential barrier problem ( particle in a box). While the "particle in a box" assumes the potential inside the box is 0, that is not the case when looking inside a solid material. ...more on Wikipedia about "One-dimensional periodic case"
In physics, the particle in a box is a very simple problem consisting of a single particle bouncing around inside of an immovable box, from which it cannot escape, and which loses no energy when it collides with the walls of the box. In classical mechanics, the solution to the problem is trivial: The particle moves in a straight line, always at the same speed, until it reflects from a wall. When it reflects from a wall, it always reflects at an equal but opposite angle to its angle of approach, and its speed does not change. ...more on Wikipedia about "Particle in a box"
In quantum mechanics, the particle in a one-dimensional lattice is an idealised system that can be solved completely with some simplifications. The one-dimensional particle lattice is a simplified expansion of the 3D infinite potential barrier (particle in a box). While the " particle in a box" assumes the potential inside the box is 0, it is not the case when looking inside a solid material. ...more on Wikipedia about "Particle in a one-dimensional lattice (periodic potential)"
In quantum mechanics, the case of a particle in a one-dimensional ring is similar to the particle in a box. The Schrödinger equation for a free particle which is restricted to a ring (technically, whose configuration space is the circle ) is ...more on Wikipedia about "Particle in a ring"
In quantum mechanics, the particle in a spherically symmetric potential describes the dynamics of a particle in a central force field, i.e. with potential depending only on the distance of the particle to the center of force (radial dependency), having no angular dependency. In its quantum mechanical formulation, it amounts to solving the Schrödinger equation with potentials V(r) which depend only on r, the modulus of r. ...more on Wikipedia about "Particle in a spherically symmetric potential"
The quantum harmonic oscillator is the quantum mechanical analogue of the classical harmonic oscillator. It is one of the most important model systems in quantum mechanics because, as in classical mechanics, a wide variety of physical situations can be reduced to it either exactly or approximately. In particular, a system near an equilibrium configuration can often be described in terms of one or more harmonic oscillators. Furthermore, it is one of the few quantum mechanical systems for which a simple exact solution is known. ...more on Wikipedia about "Quantum harmonic oscillator" I wish I had a http://www.shortopedia.com.
In quantum mechanics, the ring wave guide starts from the one dimensional, time independent Schrödinger equation: ...more on Wikipedia about "Ring wave guide"
The green plane is the x-y-plane, where two (non-interacting) electron wave-packets meet. The vertical direction shows the real part of Psi(x,y). The semi-transparent white plane in the top shows the density of detection probability, i.e, |Psi(x,y)|², as blue spots. The blue in the middle is the same again. ...more on Wikipedia about "Two interfering electron wave-packets"
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