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1-20 of 115 Search Results for

#### eigenvalue

Book Chapter

Series: AIPP Books, Professional

Published: March 2023

EISBN: 978-0-7354-2547-7

ISBN: 978-0-7354-2544-6

... Normalization condition Energy eigenstates/eigenvalues, stationary states, superposition states, eigenstates/eigenvalues of generic observables Correlation between the state of preparation (e.g., superposition of energy eigenstates), possible values obtained in a measure and relative (amplitude...

Book Chapter

Series: AIPP Books, Professional

Published: March 2023

10.1063/9780735425477_008

EISBN: 978-0-7354-2547-7

ISBN: 978-0-7354-2544-6

.../eigenvalues, stationary states, superposition states, eigenstates/eigenvalues of generic observables Correlation between the state of preparation (e.g., superposition of energy eigenstates), possible values obtained in a measure and relative (amplitude of) probability of the outcomes Change of state...

Images

**Published:**December 2022

FIG. 3.17 The eigenvalues for a two-site Kitaev model are plotted. Different choices of parameters for all the plots are to be correlated with the values of μ , t , and Δ given in Table 3.1 . The top left and the bottom right correspond to the topological and the trivial phases of ... More about this image found in The eigenvalues for a two-site Kitaev model are plotted. Different choices ...

Book Chapter

Series: AIPP Books, Principles

Published: March 2023

10.1063/9780735425590_001

EISBN: 978-0-7354-2559-0

ISBN: 978-0-7354-2556-9

... a tensor takes a diagonal form is also referred to as principal axes and the coefficients in the diagonal are called principal coefficients. Note that the eigenvalues of a second-rank tensor are the principal coefficients and the eigenvectors corresponding to these eigenvalues form the principal axes...

Book Chapter

Series: AIPP Books, Professional

Published: March 2023

10.1063/9780735425514_024

EISBN: 978-0-7354-2551-4

ISBN: 978-0-7354-2548-4

... is the selection of the number of factors. The factor analysis method used found the factors as eigenvectors of the correlation matrix. The eigenvalue associated with the eigenvector is related to the variance explained. The scree plot, Fig. 24.1 , plots the eigenvalue against the number of factors. One method...

Book Chapter

Series: AIPP Books, Principles

Published: March 2023

10.1063/9780735425590_006

EISBN: 978-0-7354-2559-0

ISBN: 978-0-7354-2556-9

... . The general form of the solution of Eq. ( 6.68 ) is (6.69) u ˜ B = a e p z . Substituting Eq. ( 6.69 ) into Eq. ( 6.68 ) yields the characteristic equation: (6.70) ( G p 2 + ( R + R T ) p + W ) a = 0. Equation ( 6.70 ) is a nonlinear eigenvalue problem...

Book Chapter

Book: Toward Better Photovoltaic Systems: Design, Simulation, Optimization, Analysis, and Operations

Series: AIPP Books, Principles

Published: March 2023

10.1063/9780735425613_005

EISBN: 978-0-7354-2561-3

ISBN: 978-0-7354-2560-6

... and determined the critical voltage of the PV system after reaching the reactive power limit. Subsequently, the minimum eigenvalue trajectory of the Jacobi matrix in the critical state under static load flow was calculated and used to analyze the performance and power quality of the transmission system...

Book Chapter

Series: AIPP Books, Principles

Published: March 2023

10.1063/9780735425590_002

EISBN: 978-0-7354-2559-0

ISBN: 978-0-7354-2556-9

... implies lower effective mass and a large carrier mobility. The Kohn–Sham energy eigenvalues obtained from a DFT calculation can be used to evaluate the conductivity tensor using the Boltzmann transport equations given by (2.11) Σ = e 2 τ ∑ n ∫ d k 4 π 3...

Book

Series: AIPP Books, Professional

Published: March 2023

10.1063/9780735425477

EISBN: 978-0-7354-2547-7

ISBN: 978-0-7354-2544-6

Book

Series: AIPP Books, Principles

Published: March 2023

10.1063/9780735425613

EISBN: 978-0-7354-2561-3

ISBN: 978-0-7354-2560-6

Book

Series: AIPP Books, Principles

Published: March 2023

10.1063/9780735425590

EISBN: 978-0-7354-2559-0

ISBN: 978-0-7354-2556-9

Book Chapter

Series: AIPP Books, Principles

Published: February 2023

10.1063/9780735425033_007

EISBN: 978-0-7354-2503-3

ISBN: 978-0-7354-2500-2

... solution of Schrödinger's and Poisson's equation for a given heterostructure yields the corresponding characteristics wavefunction and eigenvalues in the 2-DEG. Electron Transport in Bulk β-Ga

_{2}O_{3}Low field electron mobility The 10-atom primitive cell of a base-centered monoclinic...Book Chapter

Series: AIPP Books, Principles

Published: December 2022

10.1063/9780735425668_002

EISBN: 978-0-7354-2566-8

ISBN: 978-0-7354-2564-4

... ^ ) [Eq. ( 2.11 )] in an eigenvalue problem. The potential energy operator ( V ^ ) [Eq. ( 2.11 )] is set to zero in the cases presented in this text. Orthonormality and eigenvalue equations will be explained below and computed explicitly in Chap. 3, (2.9) E n = 〈 ψ n ( x ) | H...

Book Chapter

Series: AIPP Books, Principles

Published: December 2022

10.1063/9780735425668_003

EISBN: 978-0-7354-2566-8

ISBN: 978-0-7354-2564-4

... ), momentum ( p ^ ψ = ( ℏ / i ) ( d / d x ) ψ ), and energy ( H ^ ψ = − ( ℏ 2 / 2 m ) ( d 2 / d x 2 ) ψ ). Hermitian operators produce real

*eigenvalues (observables)*. Each eigenvalue is produced by a single*normalized*wave function...Book Chapter

Series: AIPP Books, Methods

Published: January 2023

10.1063/9780735425279_010

EISBN: 978-0-7354-2527-9

ISBN: 978-0-7354-2524-8

... ; Lane

*et al.*, 2013 ; Pérez-Hernández*et al.*, 2013 ; Chodera and Noe, 2014 ; and Husic and Pande, 2018 ): (10.2) t i ( τ ) = − τ ln λ i ( τ ) , where*λ*(_{i}*τ*) is the*i*-th eigenvalue of*T*(*τ*). Each implied...Book Chapter

Series: AIPP Books, Perspectives

Published: December 2022

10.1063/9780735422537_001

EISBN: 978-0-7354-2253-7

ISBN: 978-0-7354-2251-3

... 2 . Writing the problem in the (

*s*,*m*_{s}) basis [*S*^{2}has the eigenvalue*s*(*s*+ 1) and*S*_{z}has the eigenvalue*m*_{s}, with ℏ = 1 ], the direct product space ( s...Book Chapter

Series: AIPP Books, Principles

Published: December 2022

10.1063/9780735425668_001

EISBN: 978-0-7354-2566-8

ISBN: 978-0-7354-2564-4

... complex differential equations necessitated the use of the eigenvalue equation we call Schrödinger's equation [Eq. ( 1.2 )], (1.2) H ^ ψ = E ψ . FIG. 1.3 Standing waves are “pinned” to zero at the extremes and have discrete (integer) numbers of oscillating lobes,

*n*= {1, 2, 3...Book Chapter

Series: AIPP Books, Methods

Published: November 2022

10.1063/9780735422575_002

EISBN: 978-0-7354-2257-5

ISBN: 978-0-7354-2254-4

...Linear ODEs and Orthogonal Functions It has been recognized that the vast majority of the eigenvalue problems in physics lead to second-order differential equations with the general form ( Ince, 1927 ) (2.1) L ^ [ ϕ ] = R ( x ) , a ≤ x ≤ b , (2.2) L...

Book

Series: AIPP Books, Principles

Published: December 2022

10.1063/9780735425668

EISBN: 978-0-7354-2566-8

ISBN: 978-0-7354-2564-4

Book

Series: AIPP Books, Methods

Published: January 2023

10.1063/9780735425279

EISBN: 978-0-7354-2527-9

ISBN: 978-0-7354-2524-8

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