why uncertaninity in position is more when uncertanity in velocity is less?
Answers
Answer:The answer to your question would be complete uncertainty in position (the plane wave), but not possible for there to be no uncertainty. It might be helpful to walk through a plain English breakdown of the uncertainty principle (which really has a life outside of physics and is just a mathematical fact about the Fourier transform).
Explanation:
Let’s say that there are two kinds of wave functions marking two ends or extremes of some spectrum. Every other kind of wave is some mix of the two.
On one extreme, we have the plane wave (left side… simplified in that it should continue forever to the left and to the right, up and down with the same wavelength). It has no uncertainty in momentum and complete uncertainty in position. On the other extreme, we have the Dirac Delta function, which really isn’t a wave anymore (but let’s keep calling it that), but instead an infinitely tall narrow spike at a specific location. The Dirac Delta function has no uncertainty in position (it’s at a specific spot), but complete uncertainty in momentum. The plane wave is the eigenvector of the momentum operator, and the Dirac Delta function is the eigenvector of the position operator.
As it turns out, you can add up or superpose tons of plane waves together (wave functions are vectors in a vector space, vectors can be added), and get a Dirac Delta function, or superpose a ton of Dirac Delta functions to get a plane wave. You can go either direction. You can never really get the ends of the spectrum, but instead waves in the middle, which by nature, have some uncertainty in both.