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The narrow-width limit of the Gaussian wave packet solution discussed is the free propagator kernel K. For other differential equations, this is usually called the Green's function, [22] but in quantum mechanics it is traditional to reserve the name Green's function for the time Fourier transform of K.
Solitary wave in a laboratory wave channel. In mathematics and physics, a soliton is a nonlinear, self-reinforcing, localized wave packet that is strongly stable, in that it preserves its shape while propagating freely, at constant velocity, and recovers it even after collisions with other such localized wave packets.
The Slater determinant arises from the consideration of a wave function for a collection of electrons, each with a wave function known as the spin-orbital (), where denotes the position and spin of a single electron. A Slater determinant containing two electrons with the same spin orbital would correspond to a wave function that is zero everywhere.
In quantum mechanics, where all particle momenta are associated with waves, it is the formation of such a wave packet which localizes the wave, and thus the particle, in space. In states where a quantum mechanical particle is bound, it must be localized as a wave packet, and the existence of the packet and its minimum size implies a spread and ...
In fluid dynamics, the Davey–Stewartson equation (DSE) was introduced in a paper by A. Davey and Keith Stewartson to describe the evolution of a three-dimensional wave-packet on water of finite depth.
A Spacetime wave packet is a spatial-temporal light structure with a one-to-one correlation between spatial and temporal frequencies. [1] In particular, their group velocity in free space can be controlled arbitrarily from sub-luminal to super-luminal speeds without needing to control the dispersion of the medium it is propagating within. [ 2 ]
This result is an approximation that fails to capture certain interesting aspects of the evolution a free quantum particle. Notably, the width of the wave packet, as measured by the uncertainty in the position, grows linearly in time for large times. This phenomenon is called the spread of the wave packet for a free particle.
This is because the Helmholtz equation for electromagnetic waves and the time-independent Schrödinger equation have the same form. Since tunneling is a wave phenomenon, it occurs for all kinds of waves - matter waves, electromagnetic waves, and even sound waves. Hence the Hartman effect should exist for all tunneling waves.