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The Time-Dependent Schrodinger Equation: The …
178 Brazilian Journal of Physics, vol. 38, no. 1, March, 2008 The Time-Dependent Schr odinger Equation: The Need for the Hamiltonian to be Self-AdjointVanilse S. Araujo,Escola de Engenharia Maua, S ao Paulo, Brazil and Faculdade de Engenharia da Fundac ao Santo Andre, S ao Paulo, BrazilF. A. B. Coutinho,Faculdade de Medicina da Universidade de S ao Paulo, S ao Paulo, 01246-903, BrazilF. M. ToyamaDepartment of Information and Communication Sciences, Kyoto Sangyo University, Kyoto 603-85555 JapanReceived on 20 December, 2007We present some simple arguments to show that quantum mechanics operators are required to be emphasize that the very definition of a self-adjoint operator includes the prescription of a certain domain ofthe operator. We then use these concepts to revisit the solutions of the Time-Dependent Schroedinger equation ofsome well-known simple problems the infinite square well, the finite square well, and the harmonic show that these elementary illustrations can be enriched by using more general boundary conditions, whichare still compatible with self-adjointness.
178 Brazilian Journal of Physics, vol. 38, no. 1, March, 2008 The Time-Dependent Schrodinger Equation: The Need for the Hamiltonian to be Self-Adjoint¨ Vanilse S. Araujo, Escola de Engenharia Maua, Sao Paulo, Brazil and Faculdade de Engenharia da Fundac˜ ¸ao Santo Andre, S˜ ao Paulo, Brazil˜
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