Do the Schrodinger equation and Heisenberg uncertainty principle conflict?
Basically, x and p mean different things between the Scrodinger equation and the uncertainty relation. x and p as they show up in Schrodinger equation DO NOT refer to the position and the momentum of the particle. They refer to the linear operators that represent momentum and position in general. The possible outcomes of a measurement are the eigenvalues of the operator that represents it. In the uncertainty relation, delta x and delta p refer to the standard deviations of momentum and position measurements. That is, you prepared a million identical quantum systems, then you measure the position of all of the particles, and record all of the values of x. Then, you find the standard deviation of all of these measurements. That is delta x. You do the same thing again, only this time you measure momentum. The standard deviation of all of the momentum measurements is delta p. The uncertainty relation says the product of these two numbers is more than hbar/2.
