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Detail of the Catalan Atlas depicting Marco Polo travelling to the East during the Pax Mongolica. The Pax Mongolica (Latin for "Mongol Peace"), less often known as Pax Tatarica [1] ("Tatar Peace"), is a historiographical term modeled after the original phrase Pax Romana which describes the stabilizing effects of the conquests of the Mongol Empire on the social, cultural and economic life of ...
The wave envelope is the profile of the wave amplitudes; all transverse displacements are bound by the envelope profile. Intuitively the wave envelope is the "global profile" of the wave, which "contains" changing "local profiles inside the global profile".
The Mongols had threatened Europe, but Mongol states also unified much of Eurasia and, from 1206 on, the Pax Mongolica allowed safe trade routes and communication lines from the Middle East to China. [ 44 ] [ 45 ] The close Italian links to the Levant raised curiosity and commercial interest in countries which lay further east.
In 1924, the Mongolian People's Republic was declared, and Mongolian politics began to follow the same patterns as Soviet politics of the time. Following the Revolutions of 1989 , the Mongolian Revolution of 1990 led to a multi-party system , a new constitution in 1992, and a transition to a market economy .
The wave function of an initially very localized free particle. In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters ψ and Ψ (lower-case and capital psi, respectively). Wave functions are complex ...
For example, the photons emitted by a radio station broadcast at the frequency ν = 100 MHz, have an energy content of νh = (1 × 10 8) × (6.6 × 10 −34) = 6.6 × 10 −26 J, where h is the Planck constant. The wavelength of the station is λ = c/ν = 3 m, so that λ/(2π) = 48 cm and the volume is 0.109 m 3.
The wave associated with a particle of a given mass, such as an atom, has a defined frequency, and a change in the duration of one cycle from peak to peak that is sometimes called its Compton periodicity. Such a matter wave has the characteristics of a simple clock, in that it marks out fixed and equal intervals of time.
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. (Here the physics definition for the wave vector is ...