Raman spectroscopy

Grossman, William E. L.

doi:10.1021/ac60369a016

Cited by 10 publications

(4 citation statements)

References 123 publications

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“…Proof of this is given in Appendix D. It expresses the geometrical origin of the displaced parity operator [49][50][51] present in c-number functions that emulate Hilbert space operators in phase space formulation of quantum mechanics. The formula agrees with Wootters [11] where it is given as a point in what is essentially APG.…”

Section: R|p(m(b); B)|rmentioning

confidence: 99%

Finite linear spaces, plane geometries, Hilbert spaces and finite phase space

Revzen

Mann

2016

Quantum Stud.: Math. Found.

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Finite plane geometry is associated with finite dimensional Hilbert space. The association allows mapping of q-number Hilbert space observables to the c-number formalism of quantum mechanics in phase space. The mapped entities reflect geometrically based line-point interrelation. Particularly simple formulas are involved when use is made of mutually unbiased bases (MUB) representations for the Hilbert space entries.The geometry specifies a point-line interrelation. Thus underpinning d-dimensional Hilbert space operators (resp. states) with geometrical points leads to operators termed "line operators" underpinned by the geometrical lines. These "line operators",Lj ; (j designates the line) form a complete orthogonal basis for Hilbert space operators. The representation of Hilbert space operators in terms of these operators form the phase space representation of the d-dimensional Hilbert space.Examples for the use of the "line operators" in mapping (finite dimensional) Hilbert space operators onto finite dimensional phase space functions are considered. These include finite dimensional Wigner function and Radon transform and a geometrical interpretation for the involvement of parity in the mappings of Hilbert space onto phase space.Two d-dimensional particles product states are underpinned with geometrical points. The states, |Lj underpinned with the corresponding geometrical lines are maximally entangled states (MES). These "line states" provide a complete d 2 dimensional orthogonal MES basis for for the two d-dimensional particles. The complete d2 dimensional MES i.e. the "line states" are shown to provide a transparent geometrical interpretation to the so called Mean King Problem and its variant.The "line operators" (resp. "line states") are studied in detail.The paper aims at self sufficiency and to this end all relevant notions are explained herewith.

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Section: R|p(m(b); B)|rmentioning

confidence: 99%

Finite linear spaces, plane geometries, Hilbert spaces and finite phase space

Revzen

Mann

2016

Quantum Stud.: Math. Found.

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“…We can round off this discussion with a few comments about the algebraic structure behind the entire WWM-formalism. The flat space Wigner function has a natural group theoretical interpretation, [10]. Define the operator Π(u, v) = exp(iup − iv q) (122) then Π(u, v) form a ray representation of the (Abelian) group of translations in phase-space,…”

Section: Group Theoretical Argumentsmentioning

confidence: 99%

Quantum theory in curved spacetime using the Wigner function

Antonsen¹

1997

Phys. Rev. D

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A new non-perturbative approach to quantum theory in curved spacetime and to quantum gravity, based on a generalisation of the Wigner equation, is proposed. Our definition for a Wigner equation differs from what have otherwise been proposed, and does not imply any approximations. It is a completely exact equation, fully equivalent to the Heisenberg equations of motion. The approach makes different approximation schemes possible, e.g. it is possible to perform a systematic calculation of the quantum effects order by order. An iterative scheme for this is also proposed. The method is illustrated with some simple examples and applications. A calculation of the trace of the renormalised energy-momentum tensor is done, and the conformal anomaly is thereby related to non-conservation of a current in d = 2 dimensions and a relationship between a vector and an axial-vector current in d = 4 dimensions. The corresponding "hydrodynamic equations" governing the evolution of macroscopic quantities are derived by taking appropriate moments. The emphasis is put on the spin-1 2 case, but it is shown how to extend to arbitrary spins. Gravity is treated first in the Palatini formalism, which is not very tractable, and then more successfully in the Ashtekar formalism, where the constraints lead to infinite order differential equations for the Wigner functions.

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“…In the present contribution, a very specific situation is addressed, namely, Raman microscopy measurements of multiwell plates. Raman spectroscopy is a widely used analytical tool with a very wide range of applications, involving gas, liquid, and solid samples. , Multiwell plates are becoming an increasingly chosen route for high-throughput experimentation. − This situation has arisen, in part, because of the small quantities of consumable materials needed, as well as the wide variety of instrumentation that can accommodate multiwell sampling.…”

Section: Introductionmentioning

confidence: 99%

Combination of Raman Microscopy, Multiwell Plate Experimental Designs, and BTEM Analysis for High-Throughput Experimentation

Widjaja

Garland

2009

J. Comb. Chem.

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Both nonreactive and reactive multiwell plate experiments were combined with Raman microscopy and band-target entropy minimization (BTEM) analysis. The multicomponent nonreactive experiments showed that accurate pure component spectral estimation is possible without recourse to any spectral libraries. The multicomponent reactive experiments showed that, in addition to accurate pure component spectral estimation, concentration profiles can be obtained for quantitative purposes. In the present case, the solvent and time dependence of a cycloaddition reaction was addressed as the high-throughput experimentation issue. A total of 1152 experimental spectra were collected and analyzed. Two methods were used, namely, (A) each solvent set was individually analyzed and (B) the entire set of spectra, from 4 different solvents, were analyzed all together. Method B provided very satisfactory results. The present study with combined Raman-multiwell plate-BTEM analysis establishes proof of concept. The new approach appears to be applicable to other frequently conducted combinatorial/high-throughput experimentations. These include, but are not restricted to, chemo- and regioselective studies, solid-phase syntheses, etc.

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Raman spectroscopy

Cited by 10 publications

References 123 publications

Finite linear spaces, plane geometries, Hilbert spaces and finite phase space

Finite linear spaces, plane geometries, Hilbert spaces and finite phase space

Quantum theory in curved spacetime using the Wigner function

Combination of Raman Microscopy, Multiwell Plate Experimental Designs, and BTEM Analysis for High-Throughput Experimentation

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