Modification of the spectrum of the second-quantization operator under its perturbation by a potential

Various upper bounds for the L2-norm of the Wick product of two measurable functions of a random variable X, having finite moments of any order, together with a universal minimal condition, are proven. The inequalities involve the second quantization operator of a constant times the identity operator. Some conditions ensuring that the constants involved in the second quantization operators are optimal, and interesting examples satisfying these conditions are also included.

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BAYES' FORMULA FOR SECOND QUANTIZATION OPERATORS

Stochastics and Dynamics ◽

10.1142/s0219493706001748 ◽

2006 ◽

Vol 06 (02) ◽

pp. 245-253 ◽

Cited By ~ 1

Author(s):

ALBERTO LANCONELLI

Keyword(s):

Conditional Expectation ◽

Bayes Rule ◽

Second Quantization ◽

Absolutely Continuous ◽

Bayes Formula ◽

Conditional Expectations ◽

Quantization Operator ◽

Continuous Measures ◽

The Relationship ◽

Absolutely Continuous Measures

The Bayes' formula provides the relationship between conditional expectations with respect to absolutely continuous measures. The conditional expectation is in the context of the Wiener space — an example of second quantization operator. In this note we obtain a formula that generalizes the above-mentioned Bayes' rule to general second quantization operators.

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Generalization of the New Resonance Theory: Second Quantization Operator, Localization Scheme, and Basis Set

Journal of Chemical Theory and Computation ◽

10.1021/ct900053r ◽

2009 ◽

Vol 5 (7) ◽

pp. 1741-1748 ◽

Cited By ~ 6

Author(s):

Atsushi Ikeda ◽

Yoshihide Nakao ◽

Hirofumi Sato ◽

Shigeyoshi Sakaki

Keyword(s):

Basis Set ◽

Second Quantization ◽

Resonance Theory ◽

Localization Scheme ◽

Quantization Operator

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SNEG – Mathematica package for symbolic calculations with second-quantization-operator expressions

Computer Physics Communications ◽

10.1016/j.cpc.2011.05.013 ◽

2011 ◽

Vol 182 (10) ◽

pp. 2259-2264 ◽

Cited By ~ 30

Author(s):

Rok Žitko

Keyword(s):

Second Quantization ◽

Symbolic Calculations ◽

Quantization Operator

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A HÖLDER INEQUALITY FOR NORMS OF POISSONIAN WICK PRODUCTS

Infinite Dimensional Analysis Quantum Probability and Related Topics ◽

10.1142/s0219025713500227 ◽

2013 ◽

Vol 16 (03) ◽

pp. 1350022 ◽

Cited By ~ 5

Author(s):

ALBERTO LANCONELLI ◽

AUREL I. STAN

Keyword(s):

Hölder Inequality ◽

Wick Product ◽

Identity Operator ◽

Second Quantization ◽

Charlier Polynomials ◽

Quantization Operator ◽

Wick Products

An understanding of the second quantization operator of a constant times the identity operator and the Poissonian Wick product, without using the orthogonal Charlier polynomials, is presented first. We use both understanding, with and without the Charlier polynomials, to prove some inequalities about the norms of Poissonian Wick products. These inequalities are the best ones in the case of L1, L2, and L∞ norms. We close the paper with some probabilistic interpretations of the Poissonian Wick product.

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ON HEISENBERG INEQUALITY

Communications in Contemporary Mathematics ◽

10.1142/s0219199705001635 ◽

2005 ◽

Vol 07 (01) ◽

pp. 75-88

Author(s):

AUREL STAN

Keyword(s):

White Noise ◽

Unitary Operator ◽

Noise Analysis ◽

Differentiation Operator ◽

White Noise Analysis ◽

Second Quantization ◽

Quantization Operator ◽

Heisenberg Inequality

A Heisenberg inequality, involving a differentiation operator, its adjoint, and the second quantization operator of a unitary operator, is proved in the context of white noise analysis.

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Identical Particles and Second Quantization: Occupation Number Representation

10.1093/oso/9780198791942.003.0002 ◽

2018 ◽

Author(s):

Norman J. Morgenstern Horing

Keyword(s):

Occupation Number ◽

Annihilation Operator ◽

Pauli Exclusion Principle ◽

Exclusion Principle ◽

Number Representation ◽

Second Quantization ◽

Identical Particles ◽

Fundamental Properties ◽

Minimum Uncertainty ◽

Creation Operators

Focusing on systems of many identical particles, Chapter 2 introduces appropriate operators to describe their properties in terms of Schwinger’s “measurement symbols.” The latter are then factorized into “creation” and “annihilation” operators, whose fundamental properties and commutation/anticommutation relations are derived in conjunction with the Pauli exclusion principle. This leads to “second quantization” with the Hamiltonian, number, linear and angular momentum operators expressed in terms of the annihilation and creation operators, as well as the occupation number representation. Finally, the concept of coherent states, as eigenstates of the annihilation operator, having minimum uncertainty, is introduced and discussed in detail.

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