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Differential equation for orbits is solved. The orbits are shown to be conic sections. Kepler's three laws are proved. Some properties of hyperbolic orbits are derived.$\newcommand{\pp}[2][]{\frac{\partial#1}{\partial #2}} \newcommand{\PP}[2][]{\frac{\partial^2#1}{\partial #2^2}} \newcommand{\dd}[2][]{\frac{d#1}{d #2}} \newcommand{\DD}[2][]{\frac{d^2#1}{d #2^2}}$

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A particle with localized position is described by a wave packet in quantum mechanics. Taking a free Gaussian wave packet, its wave function at arbitrary time is computed. It is fund that the average value of position varies with time like position of a classical particle. The average vale of momentum remains constant and the uncertainty \(\Delta x\) increases with time.

The entropy as computed from classical statistical mechanics does not meet the requirement that it should be an extensive property. This is known as Gibbs paradox. This is resolved by noting that the correct counting of micro states must satisfy the requirement imposed by quantum mechanics on states of a system of identical particles.

It is proved that the Runge-Lenz vector \begin{equation}
\vec{N} = \vec{v} \times \vec{L} - \frac{k\vec{r}}{r}
\end{equation} is a constant of motion for the Coulomb potential \(-k/r\). 

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