Hypervirial Theorems and Exact Solutions of the Schrödinger Equation

  • F. M. Fernández
  • E. A. Castro
Chapter
Part of the Lecture Notes in Chemistry book series (LNC, volume 43)

Abstract

According to the postulates of quantum mechanics [1–5] the state of the system ψ(0) at t = 0 is related to the state of the system ψ (t) at any other time t through:
$$\psi \left( t \right) = U\left( t \right)\psi \left( 0 \right)$$
(1)
where U(t) Is an evolution operator. The reader interested In a rigorous mathematical treatment of the evolution operators and their properties is referred to Refs. 4 and 5. A comprehensive summary is given in Apendix I. It immediately follows from the properties of U(t) that
$$\psi \left( 0 \right) = U^ + \left( t \right)\psi \left( t \right)$$
(2)
where U† is the adjoint of U.

Keywords

Matrix Element Recurrence Relation Hamiltonian Operator Hermitian Operator Virial Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • F. M. Fernández
    • 1
  • E. A. Castro
    • 1
  1. 1.Instituto de Investigaciones Fisicoquímicas Teoricas y Aplicadas (INIFTA) División Química TeóricaUniversidad Nacional de La PlataLa PlataArgentina

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