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eigenvalue
1
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-Ga2O3 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 λi(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, ms) basis [S2 has the eigenvalue s(s + 1) and Sz has the eigenvalue ms, 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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