>[!summary] Single slit experiment points that particles experience wave like interactions Can be explained by the [[Uncertainty Principle]] > **Important equations:** > Describing the wavelength and momentum interaction: $\lambda \cdot p = h$ > Angles into a single slit by HCP: $\Delta P_{x}=\frac{h}{L}$ # Single Slit Particles experimentally noticed that going through one slit exhibit wave like interactions and violate F = ma. Currently believed that particle can act **both** like wave and particle, called wave-particle duality. ![[SS_1.png]] [^1] Through experiments this function was created to describe the motion noticed in experiment. Where h is a constant. $\lambda \cdot p = h $ An increase in wavelength ($\lambda$) increases the spread An increase the momentum ($p$ ) **Doesn't change** the momentum of the particle but changes the wavelength ($\lambda \propto \frac{1}{p}$) Particle acts like a wave while moving but acts like a particle when it interacts with materials. # Using HCP For One Slit To Calculate Angles If we were to use [[Uncertainty Principle]] in a situation like this where we have a slit with length L and indefinite momentum we can calculate the angle. ![[SS_2.png]] [^1] >[!warning] Assumption To derive the angle ejected into the slit we will assume the following: > >- [[Uncertainty Principle]] is valid >- Angle can be found $\theta = \frac{\Delta P_x}{ P_y}$ To find $\Delta P_x$ we use the uncertainty principle for the x direction $\Delta P_x \Delta x = \frac{h}{2\pi}$ Since x = L our uncertainty can be as big as our slit width. Simplifying and solving for Px we get (neglecting the constants terms) $\Delta P_{x}=\frac{h}{L}$ [^1]: Taken from R.Epp notes.