7.5 Exercise 16

Estimate the ground state energy of the quantum harmonic oscillator by Heisenberg’s uncertainty principle. Start by assuming that the product of the uncertainties $\Delta x$ and $\Delta p$ is at its minimum. Write $\Delta p$ in terms of $\Delta x$ and assume that for the ground state $x \approx \Delta x$ and $p \approx \Delta p ,$ then write the ground state energy in terms of x. Finally, find the value of x that minimizes the energy and find the minimum of the energy.