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If (,) (and therefore ()) is a Gaussian function, the wave packet is called a Gaussian wave packet. [12] For example, the solution to the one-dimensional free Schrödinger equation (with 2Δx, m, and ħ set equal to one) satisfying the initial condition (,) = / (+), representing a wave packet localized in space at the origin as a Gaussian ...
This wave packet becomes increasingly localized with the addition of many waves. The Fourier transform is a mathematical operation that separates a wave packet into its individual plane waves. The waves shown here are real for illustrative purposes only; in quantum mechanics the wave function is generally complex .
The Mott problem is an iconic challenge to quantum mechanics theory: how can the prediction of spherically symmetric wave function result in linear tracks seen in a cloud chamber. [1]: 119ff The problem was first formulated in 1927 by Albert Einstein and Max Born and solved in 1929 by Nevill Francis Mott. [2]
A portion of the wave packet passes through the barrier. The wave function of a physical system of particles specifies everything that can be known about the system. [8] Therefore, problems in quantum mechanics analyze the system's wave function. Using mathematical formulations, such as the Schrödinger equation, the time evolution of a known ...
In principle, any particle should be described by a wave packet, but we instead describe the scattering of a plane wave traveling along the z axis, since wave packets can be expanded in terms of plane waves, and this is mathematically simpler. Because the beam is switched on for times long compared to the time of interaction of the ...
If the momentum of the initial wave function is highly localized, the wave packet will spread slowly and the group-velocity approximation will remain good for a long time. Intuitively, this result says that if the initial wave function has a very sharply defined momentum, then the particle has a sharply defined velocity and will (to good ...
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The term "wave function" is typically used for a different mathematical representation of the quantum state, one that uses spatial coordinates also called the "position representation". [9]: 324 When the wave function representation is used, the "reduction" is called "wave function collapse".