Trotter formula - Revision history

Nice and Tidy: /* References */ Fixed broken link

2009-07-10T10:39:27Z

References: Fixed broken link

← Older revision		Revision as of 12:39, 10 July 2009
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	*[http://dx.doi.org/10.1088/0305-4470/19/9/026 R. Thieberger "On the convergence of the Trotter formula", Journal of Physics A: Mathematical and General '''19''' 1551-1554 (1986)]		*[http://dx.doi.org/10.1088/0305-4470/19/9/026 R. Thieberger "On the convergence of the Trotter formula", Journal of Physics A: Mathematical and General '''19''' 1551-1554 (1986)]
	*[http://dx.doi.org/10.1016/0375-9601(93)90701-Z Masuo Suzuki "Improved Trotter-like formula", Physics Letters A '''180''' pp. 232-234 (1993)]		*[http://dx.doi.org/10.1016/0375-9601(93)90701-Z Masuo Suzuki "Improved Trotter-like formula", Physics Letters A '''180''' pp. 232-234 (1993)]
	*[http://arxiv.org/abs/physics/~~0202003Oscar~~ Oscar Bolina " Trotter formula and thermodynamic limits", arXiv:physics/0202003v1 (3 Feb 2002)]		*[http://arxiv.org/abs/physics/0202003 Oscar Bolina " Trotter formula and thermodynamic limits", arXiv:physics/0202003v1 (3 Feb 2002)]
	[[Category: Mathematics]]		[[Category: Mathematics]]

Nice and Tidy: Slight tidy

2009-07-10T10:30:37Z

Slight tidy

← Older revision		Revision as of 12:30, 10 July 2009
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	The '''Trotter formula''' is given by (~~Ref~~.1 Eq. 5):		The '''Trotter formula''' is given by (<ref>[http://www.jstor.org/stable/2033649 H. F. Trotter "On the Product of Semi-Groups of Operators", Proceedings of the American Mathematical Society '''10''' 545-551 (1959)]</ref> Eq. 5):
	:<math>e^{-\beta (H_0 + V)} = \lim_{n \rightarrow \infty} (e^{-\beta H_0 /n} e^{-\beta V/n})^n</math>		:<math>e^{-\beta (H_0 + V)} = \lim_{n \rightarrow \infty} (e^{-\beta H_0 /n} e^{-\beta V/n})^n</math>
	where <math>H_0</math> and <math>V</math> are self-adjoint operators.		where <math>H_0</math> and <math>V</math> are self-adjoint operators. This formula is used in the [[path integral formulation]].
	==References==		==References==
	~~#H. F. Trotter "On the Product of Semi-Groups of Operators", Proceedings of the American Mathematical Society~~ '''10''' ~~545-551 (1959)~~		<references/>
	#[http://dx.doi.org/10.1143/PTP.56.1454 Masuo Suzuki "Relationship between d-Dimensional Quantal Spin Systems and (d+1)-Dimensional Ising Systems - Equivalence, Critical Exponents and Systematic Approximants of the Partition Function and Spin Correlations", Progress of Theoretical Physics '''56''' pp. 1454-1469 (1976)]		'''Related reading'''
	#[http://dx.doi.org/10.1103/PhysRevA.28.3575 Hans De Raedt and Bart De Raedt "Applications of the generalized Trotter formula", Physical Review A '''28''' 3575-3580 (1983)]		*[http://dx.doi.org/10.1143/PTP.56.1454 Masuo Suzuki "Relationship between d-Dimensional Quantal Spin Systems and (d+1)-Dimensional Ising Systems - Equivalence, Critical Exponents and Systematic Approximants of the Partition Function and Spin Correlations", Progress of Theoretical Physics '''56''' pp. 1454-1469 (1976)]
	#[http://dx.doi.org/10.1088/0305-4470/19/9/026 R. Thieberger "On the convergence of the Trotter formula", Journal of Physics A: Mathematical and General '''19''' 1551-1554 (1986)]		*[http://dx.doi.org/10.1103/PhysRevA.28.3575 Hans De Raedt and Bart De Raedt "Applications of the generalized Trotter formula", Physical Review A '''28''' 3575-3580 (1983)]
	#[http://dx.doi.org/10.1016/0375-9601(93)90701-Z Masuo Suzuki "Improved Trotter-like formula", Physics Letters A '''180''' pp. 232-234 (1993)]		*[http://dx.doi.org/10.1088/0305-4470/19/9/026 R. Thieberger "On the convergence of the Trotter formula", Journal of Physics A: Mathematical and General '''19''' 1551-1554 (1986)]
	#[http://arxiv.org/abs/physics/0202003Oscar Oscar Bolina " Trotter formula and thermodynamic limits", arXiv:physics/0202003v1 (3 Feb 2002)]		*[http://dx.doi.org/10.1016/0375-9601(93)90701-Z Masuo Suzuki "Improved Trotter-like formula", Physics Letters A '''180''' pp. 232-234 (1993)]
			*[http://arxiv.org/abs/physics/0202003Oscar Oscar Bolina " Trotter formula and thermodynamic limits", arXiv:physics/0202003v1 (3 Feb 2002)]
	[[Category: Mathematics]]		[[Category: Mathematics]]

Carl McBride: Added another reference.

2008-10-23T17:07:32Z

Added another reference.

← Older revision		Revision as of 19:07, 23 October 2008
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	#[http://dx.doi.org/10.1103/PhysRevA.28.3575 Hans De Raedt and Bart De Raedt "Applications of the generalized Trotter formula", Physical Review A '''28''' 3575-3580 (1983)]		#[http://dx.doi.org/10.1103/PhysRevA.28.3575 Hans De Raedt and Bart De Raedt "Applications of the generalized Trotter formula", Physical Review A '''28''' 3575-3580 (1983)]
	#[http://dx.doi.org/10.1088/0305-4470/19/9/026 R. Thieberger "On the convergence of the Trotter formula", Journal of Physics A: Mathematical and General '''19''' 1551-1554 (1986)]		#[http://dx.doi.org/10.1088/0305-4470/19/9/026 R. Thieberger "On the convergence of the Trotter formula", Journal of Physics A: Mathematical and General '''19''' 1551-1554 (1986)]
			#[http://dx.doi.org/10.1016/0375-9601(93)90701-Z Masuo Suzuki "Improved Trotter-like formula", Physics Letters A '''180''' pp. 232-234 (1993)]
	#[http://arxiv.org/abs/physics/0202003Oscar Oscar Bolina " Trotter formula and thermodynamic limits", arXiv:physics/0202003v1 (3 Feb 2002)]		#[http://arxiv.org/abs/physics/0202003Oscar Oscar Bolina " Trotter formula and thermodynamic limits", arXiv:physics/0202003v1 (3 Feb 2002)]
	[[Category: Mathematics]]		[[Category: Mathematics]]

Carl McBride: Added some references.

2008-10-23T16:44:00Z

Added some references.

← Older revision		Revision as of 18:44, 23 October 2008
Line 1:		Line 1:
	The '''Trotter formula''' is given by		The '''Trotter formula''' is given by (Ref.1 Eq. 5):
	:<math>e^{-\beta (H_0 + V)} = \lim_{n \rightarrow \infty} (e^{-\beta H_0 /n} e^{-\beta V/n})^n</math>		:<math>e^{-\beta (H_0 + V)} = \lim_{n \rightarrow \infty} (e^{-\beta H_0 /n} e^{-\beta V/n})^n</math>
	where <math>H_0</math> and <math>V</math> are self-adjoint operators.		where <math>H_0</math> and <math>V</math> are self-adjoint operators.
			==References==
			#H. F. Trotter "On the Product of Semi-Groups of Operators", Proceedings of the American Mathematical Society '''10''' 545-551 (1959)
			#[http://dx.doi.org/10.1143/PTP.56.1454 Masuo Suzuki "Relationship between d-Dimensional Quantal Spin Systems and (d+1)-Dimensional Ising Systems - Equivalence, Critical Exponents and Systematic Approximants of the Partition Function and Spin Correlations", Progress of Theoretical Physics '''56''' pp. 1454-1469 (1976)]
			#[http://dx.doi.org/10.1103/PhysRevA.28.3575 Hans De Raedt and Bart De Raedt "Applications of the generalized Trotter formula", Physical Review A '''28''' 3575-3580 (1983)]
			#[http://dx.doi.org/10.1088/0305-4470/19/9/026 R. Thieberger "On the convergence of the Trotter formula", Journal of Physics A: Mathematical and General '''19''' 1551-1554 (1986)]
			#[http://arxiv.org/abs/physics/0202003Oscar Oscar Bolina " Trotter formula and thermodynamic limits", arXiv:physics/0202003v1 (3 Feb 2002)]
	[[Category: Mathematics]]		[[Category: Mathematics]]

Carl McBride: New page: The '''Trotter formula''' is given by : $e^{-\beta (H_0 + V)} = \lim_{n \rightarrow \infty} (e^{-\beta H_0 /n} e^{-\beta V/n})^n$ where $H_0$ and $V$ are s...

2008-09-15T13:03:09Z

New page: The '''Trotter formula''' is given by :<math>e^{-\beta (H_0 + V)} = \lim_{n \rightarrow \infty} (e^{-\beta H_0 /n} e^{-\beta V/n})^n</math> where <math>H_0</math> and <math>V</math> are s...

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