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Wave-particle duality is the concept in quantum mechanics that fundamental entities of the universe, like photons and electrons, exhibit particle or wave properties according to the experimental circumstances. [1]: 59 It expresses the inability of the classical concepts such as particle or wave to fully describe the behavior of quantum objects ...
The simplest approach is to focus on the description in terms of plane matter waves for a free particle, that is a wave function described by =, where is a position in real space, is the wave vector in units of inverse meters, ω is the angular frequency with units of inverse time and is time.
Particle velocity (denoted v or SVL) is the velocity of a particle (real or imagined) in a medium as it transmits a wave. The SI unit of particle velocity is the metre per second (m/s). In many cases this is a longitudinal wave of pressure as with sound , but it can also be a transverse wave as with the vibration of a taut string.
This demonstrates the wave–particle duality, which states that all matter exhibits both wave and particle properties: The particle is measured as a single pulse at a single position, while the modulus squared of the wave describes the probability of detecting the particle at a specific place on the screen giving a statistical interference ...
A mechanical wave is a local deformation (strain) in some physical medium that propagates from particle to particle by creating local stresses that cause strain in neighboring particles too. For example, sound waves are variations of the local pressure and particle motion that propagate through the medium.
The wave function of the ground state of a particle in a one-dimensional well is a half-period sine wave which goes to zero at the two edges of the well. The energy of the particle is given by: h 2 n 2 8 m L 2 {\displaystyle {\frac {h^{2}n^{2}}{8mL^{2}}}} where h is the Planck constant , m is the mass of the particle, n is the energy state ( n ...
A swirling, colorful, abstract image representing the wave-particle duality of quantum mechanics. Image source: Getty Images. Just as the internet boom created giants like Amazon and Google ...
The inner product is the standard inner product on these spaces. In it, the "spin part" of a single particle wave function resides. In the non-relativistic description of an electron one has n = 2 and the total wave function is a solution of the Pauli equation.