Uniqueness of the Airy packet in quantum mechanics

Abstract

The general form of a nonspreading wave packet in one-dimensional free space is derived from first principles, employing a decomposition of the quantum mechanical evolution operator of the free particle. In agreement with the classical analysis of Berry and Balazs, the corresponding probability density is proportional to the square of an Airy function, and the packet propagates with constant acceleration.

Airy-Gauss beams and their transformation by paraxial optical systems

“…The existence of this lateral shift motivated Berry and Balazs to adopt the term accelerating for describing the Airy wave packets. Some mathematical and physical properties of the Airy wave packets were further explored by Besieris et al [5] and Unnikrishnan et al [6].…”

Airy beams beyond the paraxial approximation

“…In accord with the inherent source function (13), relative to the paraxial (scalar) treatment, we take…”

“…the Airy function-based solutions [8] of evolutionary-type equations, firstly investigated in [4,9] and later in [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] within both a quantum mechanical context (i.e. in connection with the unit-mass freeparticle Schrödinger equation) and an optical context (and hence in connection with the PWE) from a theoretical as well as an applicative viewpoint.…”

Accelerating and Abruptly-Autofocusing Beam Waves in the Fresnel Zone of Antenna Arrays

“…it represents a wavepacket that evolves without dispersing. In fact, (1) is the only dispersion-free solution of Schrödinger equation in 1D free space [2] that is localized in the sense u → 0 as x → ±∞. Second, this wavepacket moves at a constant acceleration as implied by the law x = κ 3h2 t 2 /4m 2 , which is quite peculiar taking into account the absence of forces acting on the particle.…”