The uncertainty property of electromagnetic field in optical thin microcavity

Abstract

The uncertainty property of electromagnetic field in thin microcavity is exactly derived in this paper. The intensity of the electromagnetic field at the center of thin microcavity is indeterminate while other positions intensity are determinate. The product of the deviation of momentum and the deviation of position at the center of thin microcavity is larger than a certain constant. By introducing the energy quantization condition (E=Nħω), we verify this constant has the same physical dimension as Planck’s constantħ and the value is an integral multiple of Planck’s constant, the integer is the smallest volume element at the center of thin microcavity. Furthermore, the perimeter of the smallest volume element is an integer multiple of the wavelength of the incident electromagnetic wave, which satisfies the assumption of DE Broglie matter wave. Our results are the first to find that the uncertainty property of electromagnetic field in thin microcavity and further derived the quantum uncertainty principle through the quantization of energy.