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I want to teach a kid about the difference between the interaction, Heisenberg, and Schrodinger pictures of quantum mechanics. Can I explain this concept without using equation? Is there any specific condition in which we use these pictures. If yes then what they are?

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Here's a long shot that may work for some kids.

The general idea you want to get across to kids with these three different pictures is that you can think about a physics problem in multiple different ways but still get the right answer.

Here's the analogy.The different pictures are like different ways of thinking about how the earth rotates. The physical question we are trying to answer is if someone is standing on a fixed spot on earth then how long do they have to wait for it to be light, and then go dark, and then be light again (12 hours on the equator and equinox etc. etc.)

In one picture, the solar system picture, the sun stays still in the same place but we see the earth rotating around at one revolution per 24 hours. From that we can figure out that the part of the earth the person is on is facing away from the sun for 12 hours.

In the earth picture, the earth is staying still but the sun is going around and around the sun. In this picture it takes 24 hours for the sun to go around the earth so we would also conclude the sun would be on the far side for our person for 12 hours.

The interaction picture is what someone flying in an airplane would use. Someone on an airplane would see the earth rotating backwards below them and the sun rotating forwards above them. They would need to work out some math but I think they would be able to figure out how long it takes the sun to go around someone who is standing still on the ground.

edit: If you truly want to explain the Schrodinger, Heisenberg, and interaction pictures as they're used in quantum mechanics to children, well, I don't really see the point. They are different ways of calculating mathematical quantities needed to answer physical questions in quantum mechanics. Basically the Schrodinger picture time evolves the probability distribution, the Heisenberg picture time evolves the dynamical variables and the interaction picture time evolves a little bit of both. However, I don't really expect children to understand the concepts of time evolution, probability distributions, or dynamical variables..

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  • $\begingroup$ Can you please give a bit more about the last four lines of your explanation?that you mentioned about evolution. That is for my own understanding $\endgroup$ – herry Oct 2 '18 at 7:15
  • $\begingroup$ In the Schrodinger picture the wavefunction evolves as a function of time (because of the Hamiltonian). In the Hiesenberg picture the operators evolve as a function of time (because of the Hamiltonian). In the interaction picture part of the time evolution is carried by the wavefunction and part of it is carried by the observables. The Hamiltonian is in a sense "split" between the wavefunction and the operators. If you don't understand the different pictures at this level then it will be hard to explain these things to kids. A deeper explanation may require a different question on the site. $\endgroup$ – jgerber Oct 3 '18 at 5:10
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Let the kid explore Google maps while you drive.

Schrodinger did not like the idea of the Earth moving and rotating all the time, he preferred a fixed map with North always pointing North, so our blue dot really traces a path along the fixed ground. You can think of a camera in geostationary orbit. Our position and orientation in space is the same as our position and orientation on the screen, and that changes over time.

Heisenberg however was all about the navigation mode: the camera is like a bird flying right over you, facing whichever way you're facing. Have you noticed that you stay in the same place on the screen in that mode? And it helps if you have this mentality Heisenberg had of “I want to know exactly what everything looks like around me.” They are egocentric coordinates, they turn your location into a fixed spot on the screen so that if you turn around in a circle really the map twirls around you. So our position and orientation on the screen is fixed, and our definition of what “top of the screen” means is what instead changes.

Sometimes physicists want a perspective halfway between the two: the map moves, but only very predictably. In this case the camera is a bird who follows the road at the average speed of traffic. So if you go faster than average you still move forward across the screen, if you go slower than average you're drifting backwards, if you spin around in circles the map no longer rotates especially. It still has a lot of the Heisenberg picture since it mostly follows you around and turns with you, but it has a predictable map movement, the way Schrodinger liked.

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