De Broglie wave functions

In wave mechanics the wave function 4>a(x) of a system in a state is specified by the label a. For example, in the case of a free particle a could be the momentum p, and ipa(x) would be the de Broglie wave function,... 

It is assumed that the eigenfunction (x) operated on by these infinitesimal field generators is such that the same relation (803) holds between eigenvalues of the field. In order for this to be true, the eigenfunction must be the de Broglie wave function, specifically, the phase of the classical electromagnetic field. On the 0(3) level, this is a line integral, as we have seen. 

From above de Broglie wave-function packet one can identify at f = 0 the functions... 

We are going now to further explore the influence of the non-constant amplitude dependency A k) and to see its consequences in the de Broglie wave packet evolution. However, worth using the momentum representation from de Broglie quantification in order to better emphasize on the quantum (through Planck constant dependency) influence. That is we consider the general wave function ... 

A directly application and of an extreme importance of the de Broglie wave packet is to consider its normalization by noting that the wave function in the real space and the amplitude in the reciprocal space (or of the impetus by the de Broglie quantification) are conjugate size in the sense of the Fourier mutual transforms. 

Nevertheless, one fundamental consequence of dealing with (r) as a generalized function is that it can be considering as patterning a special (generalized in the sense of resumed) wave function abstracted from the de Broglie wave-packet, namely... 

The diffraction of the electromagnetic waves or the de Broglie waves of electrons and neutrons on a liquid, liquid crystalline or crystalline structures results in a characteristic pattern from that one can restore a distribution of density in space or density function p(r) [1,2], What kind of density we speak about ... 

The full quantum nuclear wavepacket to be compared as a reference is a Gaussian function initially prepared at a position Rq, with the initial wave number ko. The width is set to = 10//co so as to be in the same order of its corresponding de Broglie wave length. The explicit form is... 

Fig. 10.5. The upper panel illustrates the long de Broglie wave at long range, on the scale of 1 fxm. The lower panel shows a blowup of the short range wave function for the case of three different potentials, with three different scattering lengths, negative, zero, and positive.

In the theory of chemical kinetics, interest has recently been limited especially to processes that can be conceived of potential theoretically or, as is sand sometimes as well, adiabatically . This means that in these processes the dynamical behaviour can essentially be characterised by a single functionj dependent only on the positions of the atomic centres of mass. This function is interpreted as a potential in the sense of classical mechanics, or, more precisely and more accurately, in the sense of wave mechanics as the determining factor for the index of refraction of the de Broglie waves of the atomic centres of mass. ... 

The energy of a de Broglie wave is inversely proportional to the square of its wavelength. The wavelength of the wave function is the value of x such that the argument of the sine function in Eq. (15.3-10) equals 2ti. 

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