Homework Statement
This integral has to do with the probability amplitude that a free particle at position x0 is found at x at some time t. With H = p2/(2m), this involves evaluating the integral
1/(2π)3∫d3p e-i(p2/(2m))t eip(x-x0)
The answer is
(m/(2πit))3/2e(im(x-x0)2)/(2t)
2...
In terms of quantum mechanics, the Dirac delta function δ(x) represents the wave function with minimum uncertainty in position. Since the Dirac delta function is basically an infinitely small spike at some position in one dimensional space, the probability of finding the particle at that point...
Say you have a gravitational acceleration between a spherical object of mass M and inner radius R and a much smaller spherical object of mass m (essentially point-like) and distance ro away (M >> m) with an acceleration on mass m at any point r given by
a = GM/r2
Knowing that the acceleration...