PHYS 1901 is one of two introductory courses on astronomy offered by Carleton (the other being PHYS 1902: From Our Stars to the Cosmos). PHYS 1901 focuses on the solar system and planetary phenomena. By the end of this course you will understand the motions of the sky, how telescopes work, the characteristics of the planets, how the solar system formed, and the methods astronomers and scientists use to learn about our neighbourhood in the Universe. I hope that you will gain a deeper appreciation of science and astronomy, and have fun learning!

\begin{aligned}
&\text { Since particle can move only in a plane, i.e., along say } x \text { and } y \text { directions then; }\
&p_{x}=n_{x} \frac{h}{2 L} \text { and } p_{y}=n_{y} \frac{h}{2 L} \text { and } p_{j}^{2}=\left(n_{x}^{2}+n_{y}^{2}\right) \frac{h^{2}}{4 L^{2}}\
&p_{j}^{2}=n_{j}^{2} \frac{h^{2}}{4 L^{2}} \text { where } n_{j}^{2}=\left(n_{x}^{2}+n_{y}^{2}\right)
\end{aligned}

Since kinetic energy of the particle $\epsilon=\frac{p^{2}}{2 m}$,
$$\epsilon_{j}=\frac{p_{j}^{2}}{2 m}=n_{j}^{2} \frac{h^{2}}{8 m L^{2}}=n_{j}^{2} \frac{h^{2}}{8 m A}$$
where $\mathrm{A}=\mathrm{L}^{2}$ is the area of the two dimensional space in which the particle is free to move. gives the desired quantized energy levels of a free particle which is confined to move in a two dimensional space.

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