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Anomalous spreading of power-Law quantum wave packets

Lillo1, Mantegna

  • 1Istituto Nazionale per la Fisica della Materia, Unita di Palermo and Dipartimento di Energetica ed Applicazioni di Fisica, Universita di Palermo, Viale delle Scienze, I-90128, Palermo, Italia.

Physical Review Letters
|October 4, 2000
PubMed
Summary

We introduce novel power-law tail quantum wave packets. Their free evolution exhibits anomalous decay and conserves finite moments, offering new insights into quantum mechanics.

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Mantegna et al. reply.

Physical review letters·1996

Area of Science:

  • Quantum mechanics
  • Theoretical physics

Background:

  • Quantum wave packets are fundamental to describing quantum systems.
  • Understanding their evolution under Hamiltonians is crucial for quantum dynamics.

Purpose of the Study:

  • Introduce and analyze power-law tail quantum wave packets.
  • Investigate their behavior as eigenfunctions of a physical Hamiltonian.
  • Characterize their free evolution dynamics, including decay properties and conserved quantities.

Main Methods:

  • Mathematical derivation of power-law tail wave packet properties.
  • Analysis of wave packet evolution using quantum mechanical principles.
  • Investigation of conserved quantities during free space evolution.

Main Results:

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  • Power-law tail wave packets are shown to be eigenfunctions of a specific Hamiltonian.
  • Anomalous asymptotic decay of the wave packet maximum is demonstrated for a range of the power-law exponent.
  • The number of finite moments of the wave packet is proven to be a conserved quantity during free evolution.

Conclusions:

  • Power-law tail wave packets represent a unique class of quantum states.
  • Their anomalous decay and conserved moments provide novel insights into quantum dynamics.
  • These findings could have implications for understanding quantum systems with specific potentials.