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Time-Dependent Variational Principle for Predicting the Expectation Value of an Observable

✍ Scribed by Balian, Roger; Vénéroni, Marcel

Book ID
118153057
Publisher
The American Physical Society
Year
1981
Tongue
English
Weight
218 KB
Volume
47
Category
Article
ISSN
0031-9007

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📜 SIMILAR VOLUMES

Time-Dependent Variational Principle for
Time-Dependent Variational Principle for the Expectation Value of an Observable: Mean-Field Applications
✍ Roger Balian; Marcel Vénéroni 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 402 KB

Given the state of a system at time t 0 , the expectation value of an observable at a later time t 1 is expressed as the stationary value of an action-like functional, in which a time-dependent state and an observable are the conjugate variables. By restricting the variational spaces, various approx

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Time-dependent variational principle for the expectation value of an observable: Mean-field applications: Roger Balian, Service de Physique Théorique, CEA, Saclay, 91191 Gif sur Yvette, France, and Marcel Vénéroni, Division de Physique Théorique, Institut de Physique Nucléaire, 91406 Orsay, France
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The linear plus Coulomb potential V(r) =ar-b/r is considered. The first-, third, and fifth-order phase-integral formulas for expectation values of integer powers of r are expressed in terms of complete elliptic integrals. It is pointed out how these results can be used to calculate the probability

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✍ Esper Dalgaard 📂 Article 📅 1980 🏛 John Wiley and Sons 🌐 English ⚖ 500 KB

## Abstract A modified form of Frenkel's time‐dependent variation principle, suggested by McLachlan for state vectors, is employed to discuss the optimal time evolution of a density operator ρ(__t__). An __ansatz__ is made for this operator such that __i__(__d__ρ/__dt__) = [__S__, ρ], where __S__(_