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IMPORTANT NOTE: The math here isn't exactly the math you would use in a formal class tackling quantum tunneling (I would know :P ), but I made this video for the 17 year old me who was SUPER EAGER to learn about quantum tunneling, but didn't know what differential equations were. I'd often get frustrated when people talked about complex physics in their videos but didn't include the math because it's "confusing", but I feel like I would've understood them more if had I been exposed to a simplified version of the math of it. Now that I've taken a formal class that talked about quantum tunneling, you can trust that the core ideas are still there. I guess you'd need to know what a couple functions look like (sine, exponential) to understand my video, but for parts that contained introductory calculus concepts, I used terms such as "rate of change" to get the ideas through. Don't worry so much about "keeping up" because I made sure to place quick segues in my video for things like: what certain terms mean timestamps you can come back to after our first pass on the math behind quantum tunneling To be honest, I EXTREMELY BELIEVE this video would be a EXCELLENT FOUNDATION for this topic, as I used the kind of symbols that I knew wouldn't remove the core idea. I also added a bit of a cool vibe, as I usually do when I make science videos, as an attempt to translate the same feelings of passion and curiosity when I study the science I'm trying to communicate. I think it's important to include that part when making science videos to remind the viewers that people involved with STEM, are people too, and maybe give off a feeling of trust towards to the scientist, and especially to the science. 0:00 Quantum tunneling and the sun are related?? The sun is made of hydrogen atoms, but how do helium, and other elements form? 0:31 Setting up an Energy position graph, defining our three regions, and what an energy barrier is 0:57 Low energy regions, and how the strong force is involved 1:30 The atom's energy, E 1:49 What "particles have wave-like properties" mean mathematically with a simple sine function 2:35 Using the total energy of a system to get a differential equation that has a fairly simple form 3:02 Solutions to our differential equation, when "E-U" is positive, and when "E-U" is negative 3:54 Using our solutions to get a more useful function, the probability function 4:44 From small scale to normal scale, adding waves, and why we don't observe big objects passing through higher energy barriers 5:10 Summary and why quantum physics is cool :P Check out other videos I also made! References Halliday, D., Resnick, R. and Walker, J. (2014) Fundamental of Physics. 10th Edition, Wiley and Sons, New York. Orzel, C. (2010). How to Teach Quantum Physics to Your Dog. Scribner. DrPhysicsA. (n.d.). Schrodinger Equation—A simple derivation. Retrieved August 13, 2021, from https://www.youtube.com/watch?v=IsX5i... PBS Space Time. (n.d.). Is Quantum Tunneling Faster than Light? | Space Time | PBS Digital Studios. Retrieved August 13, 2021, from https://www.youtube.com/watch?v=-Ifmg... Quantum Tunneling | Brilliant Math & Science Wiki. (n.d.). Retrieved August 13, 2021, from https://brilliant.org/wiki/quantum-tu... Zyga, L. & Phys.org. (n.d.). On the origins of the Schrodinger equation. Retrieved August 13, 2021, from https://phys.org/news/2013-04-schrodi... An undergrad physics student who completed a course on Modern Physics with the fly-est of colors, yours truly Beatrice Anne C. Maquilan