### Compton Frequency

^{[2]} Webster’s Dictionary provides conventional definition of a wave as “a disturbance or variation that transfers energy progressively from point to point.” In 1924, Louis-Victor de Broglie postulated that all material objects have an accompanying wave function. He also introduced Compton frequency, a kind of oscillation and circulation of the charge around a charged particle. Each object has its own specific Compton Frequency. He suggested the equation below to demonstrate the relation between wavelength of a mass and its momentum p:

λ = h/p,

Where λ is wavelength and h is the Planck constant. Previously, we speculated that the key to understanding quantum mechanics is hidden somewhere in Compton wavelength of particles.The Compton wavelength, λ, of a particle X is given by,

λ_{X} = h / m_{X}c,

where h is the Planck constant, m_{X} is the particle’s mass and c is the speed of light.

The uncertainty relation for position and momentum is shown as, Δx Δp ≥ h/2π. When the position uncertainty Δx is less than the Compton wavelength, the momentum can raise equals or greater than m_{X}c^{2}. Since momentum carries energy, when the energy gets equal or greater than m_{X}c^{2}, according to quantum field theory, two more particles are created. This takes us to the electron cloud described above. Remember that in the end we had to re-normalize and forget about the infinite amount of particles created after all.

Below we will analyze a model for a particle’s movement during its Compton wavelength. In this model, I will assume that when the particle reaches to certain velocity and energy, it disappears from space-time. The Schrödinger equation for the motion of particles along the X-axis at the time of t can be written as follows:

Ψ (x,t) = A exp[ i ( kx-ωt )]

where A is amplitude of the wave, k is the wave number, and ω is the angular velocity. We may expand the above equation as follows:

ψ (x,t) = A exp[ i ( kx-ωt )] = A cos ( kx-ωt ) + i Asin( kx-ωt )

This function is a complex number, with i Asin ( kx-ωt ) as its imaginary part. As we can see, on particle-wave function dimensions x and t are complexified (demonstrated in the complex number version) by the imaginary number i. In order to describe the particle-wave function, physics is not using the Kaluza–Klein dimension or any of the extra dimensions in string theory; instead, it has to choose a virtual figure, an imaginary dimension in order to explain wave function. Yes, we can imagine the complex numbers in our mind. However, wave function is happening all over the universe at every moment, often without presence of an imagining mind. Therefore, there should be another physical entity to accommodate the imaginary part of the complex function of the wave.

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