Phase amplitude conformal symmetry in Fourier transforms. (March 2015)

• Record Type: Journal Article
• Authors: Kuwata, S
• Is Part Of: Journal of physics. Number 597 (2015)
• Publication Date: 2015-03
• Subjects: Physics -- Congresses; 530.5
• DOI: 10.1088/1742-6596/597/1/012052
• Languages: English
• ISSNs: 1742-6588

Abstract

Abstract: For the Fourier transform ℑ : L 2 (R) → L 2 (R) of a complex-valued even or odd function ψ, it is found that the amplitude invariance | ℑ ψ | = | ψ | leads to a phase invariance or inversion as arg( ℑ ψ ) = ±arg ψ + θ ( θ = constant). The converse holds unless arg ψ = constant. The condition | ψ | = | ℑ ψ | is required in dealing with, for example, the minimum uncertainty relation between position and momentum. Without the evenness or oddness of ψ, | ℑ ψ | = | ψ | does not necessarily imply arg( ℑ ψ ) = ±arg ψ + θ, nor is the converse.