It’s not possible to KNOW that the particle is in a superposition of states since we can’t observe the superposition. The superposition idea is trying to explain what must be happening in the real world given that Schrodinger’s Wave Equation works. Schrodinger’s Wave Equation (and later upgrades like the equations of Quantum Electrodynamics) are very successful at predicting the results of quantum physics experiments. The Copenhagen Interpretation, the original interpretation of Schrodinger’s Wave Equation, describes the reality underlying the equation as a superposition.
Quantum physicists are in a situation similar to chemists before atoms could be observed with powerful microscopes. (See this article for information on our current ability to observe atoms.) Chemists predicted the results of their experiments on the assumption that atoms exist. They used atomic behavior in their calculations very successfully. Yet, for a century, from the 1800’s into the 1900’s, they had no hope of observing atoms. Some might have said that even, in principle, observation would be impossible. Similarly, many quantum physicists describe the state of quantum particles prior to detection as a superposition because doing so helps them to understand what is going on. They probably have even less hope of detecting a superposition than did chemists regarding observing an atom.
However, interestingly, I just ran across this article on a proposed 2018 experiment that may help them take a peek into the world of the superposition.
Alternatives to the Superposition Idea
The concept of the superposition is part of the Copenhagen Interpretation of quantum mechanics. But there are other explanations, for example, the de Broglie-Bohmian Interpretation, the Many Worlds interpretation, the Transactional Interpretation, and many others. Many don’t require the superposition idea.
The Superposition Idea Is Workable
The superposition idea, whether it will survive in the long run, is useful. Take the example of a photon of sunlight in photosynthesis. Plants are able to use the red photons from the sun. Red photons zip through the cells of a leaf to the “reaction center” where they provide the energy for photosynthesis, that is, the production of sugars.
The trouble is that, once absorbed by a molecule of chlorophyll, the photon must find its way through a maze of cells to find the reaction center, where it will contribute its energy. If the photon used the ordinary strategy of wandering through the maze, its energy would be lost long before it reached the reaction center. But, in fact, biologists have found that plants are able to use almost every red photon for sugar production. How?
Quantum equations to the rescue! Scientists can use quantum equations to describe what the photon actually does, which is different from wandering through a maze of cells. But what is the photon actually doing physically? The Copenhagen Interpretation is that while in a superposition, the photon is experiencing a superposition of all paths. (Richard Feynman would say that it is traveling all possible paths.) Then, it enters physical reality having selected the fastest path. Here is a 4-minute video describing this:
And here is an academic paper which gives a more technical description: Quantum mechanics explains efficiency of photosynthesis
One way to look at this is that the equations show that the photon is in a superposition. However, that’s only one look at it, the Copenhagen Interpretation way. The same equations appear in other interpretations of quantum physics and predict the same results for the red photon. There’s lots of information about these interpretations in books and on the web, starting with this Wikipedia article: Interpretations of quantum mechanics – Wikipedia