Search results
Results from the WOW.Com Content Network
In contrast to the above Gaussian wave packet, which moves at constant group velocity, and always disperses, there exists a wave function based on Airy functions, that propagates freely without envelope dispersion, maintaining its shape, and accelerates in free space: [19] = [/ ()] (/) [(/)], where, for simplicity (and nondimensionalization ...
A Gaussian function is the wave function of the ground state of the quantum harmonic oscillator. The molecular orbitals used in computational chemistry can be linear combinations of Gaussian functions called Gaussian orbitals (see also basis set (chemistry)).
In other words, it is a one-dimensional gaussian wave packet. Thus, pure states with non-negative Wigner functions are not necessarily minimum-uncertainty states in the sense of the Heisenberg uncertainty formula ; rather, they give equality in the Schrödinger uncertainty formula , which includes an anticommutator term in addition to the ...
Propagation of a wave packet demonstrating a phase velocity greater than the group velocity. This shows a wave with the group velocity and phase velocity going in different directions. The group velocity is positive, while the phase velocity is negative. [1] The phase velocity of a wave is the rate at which the wave propagates in any medium.
The average photon numbers of the three states from top to bottom are n =4.2, 25.2, 924.5 [5] Figure 2: The oscillating wave packet corresponding to the second coherent state depicted in Figure 1. At each phase of the light field, the distribution is a Gaussian of constant width. Figure 3: Wigner function of
The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the modulation or envelope of the wave—propagates through space. For example, if a stone is thrown into the middle of a very still pond, a circular pattern of waves with a quiescent center appears in the water, also known as ...
In physics, a squeezed coherent state is a quantum state that is usually described by two non-commuting observables having continuous spectra of eigenvalues.Examples are position and momentum of a particle, and the (dimension-less) electric field in the amplitude (phase 0) and in the mode (phase 90°) of a light wave (the wave's quadratures).
The phase-space formulation is a formulation of quantum mechanics that places the position and momentum variables on equal footing in phase space.The two key features of the phase-space formulation are that the quantum state is described by a quasiprobability distribution (instead of a wave function, state vector, or density matrix) and operator multiplication is replaced by a star product.