Quantum mechanics path integrals

Continues the quantum mechanical path integral modeling with the specialized Fe5mman-Kleinert variational formalism leading to a comprehensive understanding of atomic stability ... 

Voth G 1996 Path integral centroid methods Advances in Chemical Physics, New methods in Computational Quantum Mechanics vol XCIII, ed I Prigogine and S A Rice... 

Voth G A 1993 Feynman path integral formulation of quantum mechanical transition state theory J. Phys. Chem. 97 8365... 

In this section we look briefly at the problem of including quantum mechanical effects in computer simulations. We shall only examine tire simplest technique, which exploits an isomorphism between a quantum system of atoms and a classical system of ring polymers, each of which represents a path integral of the kind discussed in [193]. For more details on work in this area, see [22, 194] and particularly [195, 196, 197]. 

Feynman R P and Hibbs A R 1965 Quantum Mechanics and Path Integrals (New York McGraw-Hill)... 

Tuckerman M E and Hughes A 1998 Path integral molecular dynamics a computational approach to quantum statistical mechanics Classical and Quantum Dynamics In Condensed Phase Simulations ed B J Berne, G Ciccotti and D F Coker (Singapore World Scientific) pp 311-57... 

Feynman, R.P., Hibbs, A.R. Quantum Mechanics and Path Integrals. McGraw-Hill, New York (1965). 

H. Kleinert, Path integrals in quantum mechanics, statistics and polymer physics , World Scientific, Singapore, 1995, chapters 18.5 and 18.6. 

The path-integral quantum mechanics relies on the basic relation for the evolution operator of the particle with the time-independent Hamiltonian H x, p) = -i- V(x) [Feynman and... 

The original idea of approximating the quantum mechanical partition function by a classical one belongs to Feynman [Feynman and Vernon 1963 Feynman and Kleinert 1986]. Expanding an arbitrary /S-periodic orbit, entering into the partition-function path integral, in a Fourier series in Matsubara frequencies v . 

If we fix a realization of the path Q(x), then, when performing the path integration over q, the particle may be treated as acted on by a time-dependent potential V-miiQix), q). From traditional quantum mechanics it is clear that this integration is equivalent to the solution of the time-dependent Shrodinger equation in imaginary time. 

H. Kleinert. Path Integrals in Quantum Mechanics, Statistics and Polymer Physics. Singapore World Scientific, 1990. 

Lee s discretization of nonrclativistic quantum mechanics is almost as straightforward as the discretization of classical mechanics discussed above he uses Feynman s path integral formalism [feyn65b]. 

Feynman RP, Hibbs AR (1965) Quantum Mechanics and Path Integrals. McGraw-Hill New York, p xiv, 365 p. For the applications in quantum statistics, see chapters 10 and 11 Corrections to the errata in the book http //www.oberlin.edu/physics/dstyer/FeynmanHibbs/ and http //www.physik. fu-berlin.de/ kleinert/Feynman-Hibbs/... 

Kleinert H (2004) Path integrals in quantum mechanics, statistics, polymer physics, and financial markets. 3rd edition. World Scientific Singapore River Edge, NJ, p xxvi, 1468 p. For the quantum mechanical integral equation, see Section 1.9 For the variational perturbation theory, see Chapters... 

There is considerable interest in the use of discretized path-integral simulations to calculate free energy differences or potentials of mean force using quantum statistical mechanics for many-body systems [140], The reader has already become familiar with this approach to simulating with classical systems in Chap. 7. The theoretical basis of such methods is the Feynmann path-integral representation [141], from which is derived the isomorphism between the equilibrium canonical ensemble of a... 

Schweizer, K.S. Stratt, R.M. Chandler, D. Wolynes, P.G., Convenient and accurate discretized path integral methods for equilibrium quantum mechanical calculations, J. Chem. Phys. 1981, 75, 1347-1364... 

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