What does the graph say? what's on the x and y axis?
The x axis is position. The y axis is energy. The blue box is a potential energy barrier. The red curve shows the wavefunction of a particle at a certain energy level coming in and tunneling through the wall. (the wavefunction actually live on a different y-scale from this plot and is only superimposed here for illustrative purpose, so don’t use the energy y-scale to read into the amplitude of the oscillatory part).
more info: https://en.m.wikipedia.org/wiki/Quantum_tunnelling
I think this is quantum mechanics. Ψ(x) is the wave function of some quantum object (like an electron) as a function of (1 dimensional) space, U(x) is the potential as a function of space. Ψ(x) is a generalization of the state of a particle (a vector in a real space) for quantum mechanics (to a complex function). The squared magnitude of Ψ(x) can be interpreted (with suitable normalization) as a probability that the object will be measured to be located at x. The plot here actually shows the real component of the wave function; in general, it is complex, and it is complex in this situation.
Classically, if something is on the left side of the barrier created by U(x), it shouldn't be able to cross to the other side at all without being supplied external energy. Intuitively, imagine that I roll a literal ball to the right. You would expect it to bounce back at you. However, in quantum mechanics, it totally can appear on the other side of the barrier. Why? Based on the graph, the wave function has some nonzero magnitude on the right side of the barrier.
So this meme implies that some of the swords are going to appear on the other side of the wall.
Psi vs distance, if it's the Schrödinger equation?
The red curve is real part of Psi 😉.
