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Variational Methods for Schrödinger Type Equations

In: Current Trends in Mathematical Analysis and Its Interdisciplinary Applications

Author

Listed:
  • Giovany Malcher Figueiredo

    (Universidade de Brasilia, Departamento de Matemática)

  • Edwin Gonzalo Murcia

    (Pontificia Universidad Javeriana, Departamento de Matemáticas)

  • Gaetano Siciliano

    (Universidade de São Paulo, Instituto de Matemática e Estatística)

Abstract

It is well known that the Schrödinger equation is one of the most important equations in physics. It was formulated by E. Schrödinger in 1925 (which later in 1933 received the Nobel Prize in Physics) and introduced by taking into account the de Broglie hypothesis according to which matter particles possess a wave packet delocalized in space. According to the Copenhagen interpretation the square modulus of the wave function ψ : ℝ 3 × ℝ → ℂ $$\psi :\mathbb R^{3}\times \mathbb R\to \mathbb C$$ encloses the physical information on the particle; in particular, |ψ|2 is related to the probability of finding the particle in a specific space region. Since its formulation the Schrödinger equation is the object of many research from a physical and mathematical point of view.

Suggested Citation

  • Giovany Malcher Figueiredo & Edwin Gonzalo Murcia & Gaetano Siciliano, 2019. "Variational Methods for Schrödinger Type Equations," Springer Books, in: Hemen Dutta & Ljubiša D. R. Kočinac & Hari M. Srivastava (ed.), Current Trends in Mathematical Analysis and Its Interdisciplinary Applications, chapter 0, pages 565-645, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-15242-0_16
    DOI: 10.1007/978-3-030-15242-0_16
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