Chapter 29, Problem 71PE

Derive the approximate form of Heisenberg's uncertainty principle for energy and time, $\Delta E\Delta t\approx h$, using the following arguments: Since the position of a particle is uncertain by $\Delta x\approx \lambda$, where $\lambda$ is the wavelength of the photon used to examine it, there is an uncertainty in the time the photon takes to traverse $\Delta x$. Furthermore, the photon has an energy related to its wavelength, and it can transfer some or all of this energy to the object being examined. Thus the uncertainty in the energy of the object is also related to $\lambda$. Find $\Delta t$ and $\Delta E$ ; then multiply them to give the approximate uncertainty principle.