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The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. Schrödinger...
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The Uncertainty Principle04:08

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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Published on: June 8, 2018

Exact factorization of the time-dependent electron-nuclear wave function.

Ali Abedi1, Neepa T Maitra, E K U Gross

  • 1Max-Planck Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany.

Physical Review Letters
|September 28, 2010
PubMed
Summary
This summary is machine-generated.

We developed a method to precisely separate nuclear and electronic wave functions under time-dependent potentials. This approach defines a time-dependent potential energy surface (TDPES) useful for studying molecular dissociation, like in H(2)(+).

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Published on: August 22, 2017

Area of Science:

  • Quantum mechanics
  • Molecular physics
  • Computational chemistry

Background:

  • Accurately describing electron-nuclear dynamics is crucial for understanding chemical reactions and molecular properties.
  • Time-dependent external potentials, such as laser fields, significantly alter molecular behavior.
  • Existing models often involve approximations that limit their applicability.

Purpose of the Study:

  • To derive an exact decomposition of the molecular wave function for systems in time-dependent external potentials.
  • To rigorously define a time-dependent potential energy surface (TDPES) and geometric phase.
  • To demonstrate the utility of the TDPES in interpreting molecular dissociation mechanisms.

Main Methods:

  • Exact decomposition of the complete wave function into nuclear and electronic components.
  • Derivation of formally exact equations for the time evolution of nuclear and electronic wave functions.
  • Application of the formalism to the H(2)(+) molecular ion in a laser field.

Main Results:

  • An exact mathematical framework for separating nuclear and electronic wave functions under time-dependent external potentials.
  • Rigorous definitions of the time-dependent potential energy surface (TDPES) and time-dependent geometric phase.
  • Identification of distinct dissociation mechanisms in H(2)(+) using the TDPES as an interpretive tool.

Conclusions:

  • The exact decomposition provides a rigorous theoretical foundation for studying non-adiabatic dynamics.
  • The TDPES is a valuable concept for understanding complex molecular processes influenced by external fields.
  • This work offers new insights into laser-induced molecular dissociation.