Consider a particle with mass, m moving in one dimensional potential U=kx^2/2 as in a mass-spring system. The total energy of the particle is
E= (p^2/2m) + (kx^2/2)
Classically, the absolute minimum of the enrgy, E=0 is acheived when p=0 and x=0. In quantum mechanics however, the momentum, p and the co-ordinate x cannot simulataneously have certain valus. Using the Heisenberg uncertainty relation:
a)Calculate the minimum possible value of energy, E. This lowest possible energy, which is not zero, is called zero-point energy.
b)What is the ratio of kinetic to the potential enrgy of the particle in a state of minimal total energy
Delta x delta p = hbar / 2 <---Hesinberg Uncertainty Principle
The Attempt at a Solution
I'm completely lost, with all the remaining 4 questions of my work which I'm posting.