scholarly journals EXCITATION SPECTRA OF SPIN MODELS CONSTRUCTED FROM QUANTIZED AFFINE ALGEBRAS OF TYPES ${\rm B}_n^{\left( 1 \right)}$ and $D_n^{\left( 1 \right)}$

1996 ◽  
Vol 11 (11) ◽  
pp. 1975-2017 ◽  
Author(s):  
BRIAN DAVIES ◽  
MASATO OKADO
Keyword(s):  
Matrix Theory ◽  
The Other ◽  
Vector Representation ◽  
Excitation Spectra ◽  
Spin Models ◽  
S Matrix ◽  
Affine Algebras ◽  
Momentum Spectra ◽  
Explicit Realization ◽  
Energy And Momentum

The energy and momentum spectra of the spin models constructed from the vector representation of the quantized affine algebras of types [Formula: see text] and [Formula: see text] are computed using the approach of Davies et al.1 The results are for the antiferromagnetic (massive) regime, and they agree with the mass spectrum found from the factorized S matrix theory by Ogievetsky et al.2 The other new result is the explicit realization of the fusion construction for the quantized affine algebras of types [Formula: see text] and [Formula: see text].

CALCULATION OF EXCITATION SPECTRA OF THE SPIN MODEL RELATED WITH THE VECTOR REPRESENTATION OF THE QUANTIZED AFFINE ALGEBRA OF TYPE $A_n^{(1)} $

1994 ◽  
Vol 09 (03) ◽  
pp. 399-417 ◽  
Author(s):  
ETSURO DATE ◽  
MASATO OKADO
Keyword(s):  
Spin Model ◽  
Vector Representation ◽  
Affine Algebra ◽  
Excitation Spectra ◽  
Creation And Annihilation Operators ◽  
Type Formula ◽  
Commutation Relations ◽  
Energy And Momentum

The energy and momentum of the spin model related to the vector representation of the quantized affine algebra of type [Formula: see text] are computed in the framework of Davies et al. Commutation relations among creation and annihilation operators are also derived.

Energy and Momentum Eigenspectrum of the Hulthén-screened Cosine Kratzer Potential Using Proper Quantization Rule and SUSYQM Method

2021 ◽  
Author(s):  
Kaushal R Purohit ◽  
Rajendrasinh H PARMAR ◽  
Ajay Kumar Rai
Keyword(s):  
Quantum Mechanics ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Numerical Data ◽  
Time Dependent ◽  
Quantization Rule ◽  
Approximation Approach ◽  
Momentum Spectra ◽  
Energy And Momentum ◽  
Three Dimensional Space

Abstract Using the Qiang-Dong proper quantization rule (PQR) and the supersymmetric quantum mechanics approach, we obtained the eigenspectrum of the energy and momentum for time independent and time dependent Hulthen-screened cosine Kratzer potentials. For the suggested time independent Hulthen-screened cosine Kratzer potential, we solved the Schrodinger equation in D dimensions (HSCKP). The Feinberg-Horodecki equation for time-dependent Hulthen-screened cosine Kratzer potential was also solved (tHSCKP). To address the inverse square term in the time independent and time dependent equations, we employed the Greene-Aldrich approximation approach. We were able to extract time independent and time dependent potentials, as well as their accompanying energy and momentum spectra. In three-dimensional space, we estimated the rotational vibrational (RV) energy spectrum for many homodimers ($H_2, I_2, O_2$) and heterodimers ($MnH, ScN, LiH, HCl$). We also used the recently introduced formula approach to obtain the relevant eigen function. We also calculated momentum spectra for the dimers $MnH$ and $ScN$. The method is compared to prior methodologies for accuracy and validity using numerical data for heterodimer $LiH, HCl$ and homodimer $I_2, O_2,H_2$. The calculated energy and momentum spectra are tabulated and analysed.

scholarly journals Multi-Bloch vector representation of the qutrit

2011 ◽  
Vol 11 (5&6) ◽  
pp. 361-373
Author(s):  
Pawel Kurzynski
Keyword(s):  
Quantum State ◽  
Quantum Systems ◽  
Quantum States ◽  
The Other ◽  
Two Dimensional ◽  
Bloch Vector ◽  
Vector Representation ◽  
Alternative Approach ◽  
Complete Set

An ability to describe quantum states directly by average values of measurement outcomes is provided by the Bloch vector. For an informationally complete set of measurements one can construct unique Bloch vector for any quantum state. However, not every Bloch vector corresponds to a quantum state. It seems that only for two-dimensional quantum systems it is easy to distinguish proper Bloch vectors from improper ones, i.e. the ones corresponding to quantum states from the other ones. I propose an alternative approach to the problem in which more than one vector is used. In particular, I show that a state of the qutrit can be described by the three qubit-like Bloch vectors.

S-Matrix Theory of Currents. I

1969 ◽  
Vol 178 (5) ◽  
pp. 2245-2253
Author(s):  
R. OMNès
Keyword(s):  
Matrix Theory ◽  
S Matrix

S-matrix Theory

2020 ◽  
pp. 622-675
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Matrix Theory ◽  
Point Of View ◽  
Integrable Models ◽  
Geometrical Interpretation ◽  
Coupling Constants ◽  
Two Dimensional ◽  
Recursive Structure ◽  
Mathematical Point ◽  
S Matrix ◽  
Dynamical Principle

Chapter 17 discusses the S-matrix theory of two-dimensional integrable models. From a mathematical point of view, the two-dimensional nature of the systems and their integrability are the crucial features that lead to important simplifications of the formalism and its successful application. This chapter deals with the analytic theory of the S-matrix of the integrable models. A particular emphasis is put on the dynamical principle of bootstrap, which gives rise to a recursive structure of the amplitudes. It also covers several dynamical quantities, such as mass ratios or three-coupling constants, which have an elegant mathematic formulation that is also of easy geometrical interpretation.

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