Self-accelerating parabolic cylinder waves in 1-D

Abstract

We introduce a new self-accelerating wave packet solution of the Schrodinger equation in one dimension. We obtain an exact analytical parabolic cylinder wave for the inverted harmonic potential. We show that truncated parabolic cylinder waves exhibits their accelerating feature.

Nondiffracting gravitational waves

“…Nondiffracting wave-packets have been a fruitful field of study in quantum mechanics [1,2,49,50], electromagnetism and optics [3][4][5][6][7][8][9][10][11]. The solutions (4) and ( 9) presented along this work are in the same spirit, and complement others solutions for structured gravitational beams, as Bessel or Laguerre-Gauss, found in linearized general relativity [51,52].…”

“…Nondiffracting wave-packets are known solutions to Schrödinger equation [1,2] and Maxwell equations [3,4], and several experimental studies have been dedicated to them [3][4][5][6][7][8][9][10][11]. These solutions have been observed in experiments and some of their properties have been determined.…”

A new approach to solving the Schrödinger equation

“…The wave packet experiences a deceleration given by −ζ 0 β 3 exp(−ωt)/m 2 . With this, we have generalized the results presented in [21].…”

Nondiffracting gravitational waves

“…where Ai is an Airy function. Thus, the nondiffracting accelerating gravitational wavepacket is the real part of full solution (2). This wavepacket has an acceleration equal to k/2, deflecting its trajectory in a parabolic path in the y − ζ plane [3,15].…”

“…Nondiffracting wavepackets are known solutions to Schrödinger equation [1,2] and Maxwell equations [3,4], and several experimental studies have been dedicated to them [3][4][5][6][7][8][9][10][11]. Nevertheless, studying the implications of their existence on gravitational wave propagation seems to have been neglected so far.…”