Since 1990, based on the Type Ia Supernova observations, it was established that our universe is dominant with some unknown quantities which generally referred to as Dark Matter and Dark Energy. The term dark has been used to represent the form of quantity which does not interact with light or mainly any known particles. Since, the unknown substance is electromagneticaly neutral, hence the unknown sector has been dubbed as a dark sector. The dark matter is referred to as a form of substance which is essential for structure formation and found to be pressureless. This form of matter can be considered as a gravitating system, which behaves as a dust matter. While the form of dark energy can exhibit a repulsive effect (opposite to the gravitational force), that can generate negative pressure, making universe to grow bigger and bigger with an acceleration. It has been found that the major constituents of our universe is dark energy which is 70%, then dark matter 26% and then rest of the matter from which all the galaxies and visible structures are made of.
Scattering Amplitude Spinless Particle we are dealing with quantum description of scattering. Elastic Scattering $ \rightarrow $ between two spinless, non-relativistic particles of masses m1 and m2. During the scattering process, the particles interact with one another. If the interaction is time independent, we can describe the two-particle system with stationary states. \begin{equation}\Psi\left(\vec{r}_{1}, \vec{r}_{2}, t\right)=\psi\left(\vec{r}_{1}, \vec{r}_{2}\right) e^{-i E_{T} t / n}\end{equation} $ E_T $ is total energy. \begin{equation}\left[-\frac{\hbar^{2}}{2 m_{1}} \vec{\nabla}_{1}^{2}-\frac{\hbar^{2}}{2 m_{2}} \vec{\nabla}_{2}^{2}+\hat{V}\left(\vec{r}_{1}, \vec{r}_{2}\right)\right] \psi\left(\vec{r}_{1}, \vec{r}_{2}\right)=E_{T} \psi\left(\vec{r}_{1}, \vec{r}_{2}\right) \end{equation} defining $ ...
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