How to experience Quantum mechanical state?

Short questions do not present an issue clearly. So I believe you are asking to know what a state (a specified condition) of Quantum mechanics could be. A quick answer is the "Wave-particle duality". For example, when photons or electrons pass through 2 slits, there will be an interference pattern coming out from the slits and going onto a screen. You would see many vertical lines side by side with small gaps between them on the screen, which is evidence of waves hitting the screen.
However, if a detector were to be positioned next to where the photons or electrons are going through the two slits, it seems that the rays passing there would "realize" they are being "watched" and so behave as particles: you would then see only two vertical lines on the screen where they deposited, and with no interference pattern (the wave-like design of ripples going out of the slits.)

If you have a question, please feel free to ask it.  Why do you never ask a question?

Turn Yourself into a Proton

The same may be asked. How do you experience arithmetic and algebra? Quantum mechanics is a mathematical method.