Heisenberg's Uncertainty Principle states that we cannot simultaneously measure both the position and momentum of an object better than a certain accuracy. This limitation is not a consequence of imperfect technology, but is a fundamental law. It applies to all objects -- photons, electrons, baseballs, etc. See Halliday, section 39-8.
A highly monochromatic, continuous beam of laser light of wavelength nm passes through an electro-optic shutter. The shutter opens and closes in a time interval of Dt = ps (1 picosecond = 10-12 seconds).
a) After passing through the shutter what is the average wavelength of the photons?
l0 = nm
b) After passing through the shutter to what uncertainty, Dx, have the photons been localized? Here by Dx we mean the difference between the biggest and smallest x. (In this course we are not trying to be precise about the uncertainty, although one can be.)
Dx = m
c) After passing through the shutter what is the minimum possible fractional spread (uncertainty), Dp/p0, of photon momentum? (Here and in (d) we accept answers within a range of about a factor of ten, so that you don't have to worry about a precise definition of Dp.)
Dp/p0 =
d) After passing through the shutter what is the minimum possible spread (uncertainty) of photon wavelength?
Dl = nm
