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## Homework Statement

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

## Homework Equations

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.