Alright kiddo, let's say you have a toy car and you want to know where it will be after you push it. You can use something called equations to help you figure it out. Now, imagine you have a tiny toy car that is really, really, REALLY small, like smaller than a piece of dust. It's so small that you can't see it with your eyes or even with a microscope. This tiny car is so small that it actually follows a different set of rules than the ones we are used to with regular-sized objects.
One rule that this tiny car follows is called the Schrödinger equation. This equation helps us understand how tiny objects, like atoms and particles, move and interact with each other. But sometimes, we need a different version of the Schrödinger equation because the tiny object is moving in a special way. This is where the logarithmic Schrödinger equation comes in.
The logarithmic Schrödinger equation is a special version of the Schrödinger equation that is used when the tiny object is moving in a way that changes a lot over time. Think of it like this - when you push your toy car, it goes faster and faster, right? Well, imagine that your tiny car is going much faster than that and it's changing speed really quickly too.
The logarithmic Schrödinger equation helps us figure out where this tiny car will be at different times, even though it's moving really fast and changing speed a lot. It's called "logarithmic" because it uses a special math trick called logarithms to help us solve the equation.
So, to sum it up, the logarithmic Schrödinger equation is a special equation that helps us figure out where very tiny objects will be at different times when they're moving really quickly and changing speed a lot. It's like trying to predict where a toy car that's going super fast and speeding up and slowing down a lot will be as it moves.