Heisenberg’s uncertainty principle (Heisenberg 1927) is of fundamental importance to optics and to laser optics in particular. Here, optical arguments are applied to outline an approximate derivation of the uncertainty principle.
The quantum energy of a particle is given by the well-known quantum energy equation
h is Planck’s constant
Equating this to the relativistic energy E = mc2 and using the identity λ = c/ν, an expression for the momentum of a particle can be given as
which, using the identity
can be restated as
This momentum equation was applied to particles, ...