We've talked about the Schrödinger equation before, but we really didn't dig into it with any depth at all. Now it's time to really get in there and do the math. What is the Hamiltonian operator? What is the time-independent Schrödinger...

As we continue our search for earth-like, potentially habitable worlds, we come across an interesting triple-star system called Gliese 667. The smallest of these three stars, Gliese 667 C, is a red dwarf with several planets, one of...

Our solar system has just one star in it, the sun. But this is actually not the most common situation for systems. Most systems are multi-star systems, with binary systems being extremely common. These are systems where two stars orbit...

We've learned a bit about quantum mechanics from a strictly conceptual and qualitative standpoint. But now it's time to dig a little deeper. Quantum mechanics is mathematics, so if we want to understand it on a fundamental level, we have...

Okay, we've all dreamed about exploring the universe and finding our own little cosmic vacation bungalow. But these places are really far, so how can we get there? Not the way we go through space now, that's just too slow. Are there...

We learned a bit about general relativity and the curvature of spacetime, both earlier in this series, as well as in the modern physics course. But let's talk a bit more about the astronomical observations that corroborate this theory....

Now that we understand the Schrödinger equation, it's time to put it to good use, and solve a quantum problem. Let's find the eigenfunctions and eigenenergies associated with a quantum particle restricted to an infinite square well. This...

In the previous tutorial we solved the Schrödinger equation for a quantum particle in an infinite square well. This is also known as the problem of the particle in a box. But there is a lot to unpack regarding the results, enough to...

Have you ever seen images of colorful, wispy clouds of gas in space? Those are called nebulae! What happens inside a nebula? In some of them, new stars are born. How does that work? How can we see all this gas? Are there different types...

We are beginning to get a glimpse of quantum mechanical principles from a rigorous, mathematical perspective. Now that we know how to use operators in conjunction with wavefunctions, let's get a better sense of what wavefunctions...

Apart from all the planets in the solar system, we've discussed smaller objects as well, like asteroids and comets, and also dwarf planets. While Pluto is the most famous dwarf planet, Eris is actually slightly more massive, making it...

One type of object that some astronomers study is called a quasar. When these were first discovered, it was a bit confusing as to precisely what they are, which is why quasar stands for quasi-stellar object, since we thought they looked...

When we eventually develop the capacity to leave our solar system, we will be ready to visit countless other worlds. Where will we go first? Probably the closest system to ours, since it'll be the fastest. Which system is that? The Alpha...

We've briefly discussed exoplanets and some methods that we can use to detect them, but we haven't yet looked at any specific ones. You may have heard of the TRAPPIST-1 system that was discovered recently, and for good reason, it's a...

We've learned about the stellar life cycle, so we know what happens to smaller stars like ours, and we know what happens to larger stars that become neutron stars and black holes. But what are the limits on either side? How small can a...

We all know that the universe is big. But how big it is? Much bigger than you think. Let's start out by looking at the Earth, and then zoom out to progressively larger and larger structures, so that we can see just how big it is. Then...