Now, if you’ve been following along with our physics tutorial series so far, you might be thinking to yourself: “Hey, wait a minute! We haven’t even covered what the ***** ‘E < V0' means yet!" To start let's define our terms. E is the energy of a particle (in joules or electron volts), while V0 is the potential difference between two points in an electric field (also measured in volts). So, when we say "E < V0," what we really mean is that the kinetic energy (KE) of our little friend here is less than the amount of potential energy it would gain if it were to move from one point to another. Now, let's get back to ψ. This variable represents the probability amplitude for a particle to be found in a particular region of space at a given time. In other words, it tells us how likely our friend is going to show up in this specific spot. But why do we care about this? Well, because if we can calculate ψ, we can use it to predict the probability that our little buddy will be found somewhere else later on (which is pretty ***** cool). So, let's say we want to find out what the probability amplitude is for a particle with an initial energy of E to be located in a region between x and x+dx at time t. To do this, we need to solve Schrödinger's equation (which looks like this: 22ψ/x2 + [E V(x)]ψ = 0), but that's a topic for another day. For now, let's just assume that we have already solved it and found our solution in the form of a wave function (which is represented by the Greek letter psi). Now, to calculate ψ at time t, we need to integrate this wave function over the region between x and x+dx. This gives us: x^(x+dx)psi(x,t)dx But wait! We're not done yet. To get our probability amplitude (which is what we really care about), we need to take the absolute value of this integral squared and normalize it by dividing it by the total probability (which is represented by the constant C). This gives us: |x^(x+dx)psi(x,t)dx|^2/C The probability amplitude for a particle with an initial energy of E to be located in a region between x and x+dx at time t. Pretty cool, huh? Of course, this is just the tip of the iceberg when it comes to solving Schrödinger's equation and calculating ψ. But hey, we can't cover everything in one tutorial! So stay tuned for our next installment, where we'll dive deeper into the world of quantum mechanics and explore some more mind-bending concepts (like entanglement and superposition).