In mathematics, a Hamiltonian matrix is a 2n-by-2n matrix A such that JA is symmetric, where J is the skew-symmetric matrix J = [ 0 n I n − I n 0 n ]...

algorithm that attempts to find the lowest-energy matrix product state wavefunction of a Hamiltonian. It was invented in 1992 by Steven R. White and it...

for a dynamical system Hamiltonian path, a path in a graph that visits each vertex exactly once Hamiltonian matrix, a matrix with certain special properties...

theory, the matrix element refers to the linear operator of a modified Hamiltonian using Dirac notation. It is in fact referring to the matrix elements of...

In linear algebra, a skew-Hamiltonian matrix is a specific type of matrix that corresponds to a skew-symmetric bilinear form on a symplectic vector space...

_{3}} . The Luttinger-Kohn Hamiltonian D j j ′ {\displaystyle \mathbf {D_{jj'}} } can be written explicitly as a 8X8 matrix (taking into account 8 bands...

theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle (or...

mathematics and physics, a Hamiltonian vector field on a symplectic manifold is a vector field defined for any energy function or Hamiltonian. Named after the physicist...

the operators in the Heisenberg picture with the Hamiltonian H' = H0. The evolution of the density matrix in the interaction picture is i ℏ d d t ρ I ( t...

bra-ket-enclosed Hamiltonians is a more generalized version of this matrix. One might ask why it is necessary to write the Hamiltonian matrix in such a general...

of angular momentum. The complex conjugate of the D-matrix is an eigenfunction of the Hamiltonian of spherical and symmetric rigid rotors. The letter...

sum of terms for each electron in the molecule. The off-diagonal Hamiltonian matrix elements are given by an approximation due to Wolfsberg and Helmholz...

general Hamiltonian, if G ( t ) {\displaystyle G(t)} is the wavefunction propagator over some interval, then the time evolution of the density matrix over...

eigenvalues of the Hamiltonian matrix. Second, in the simplest case of a planar, unsaturated hydrocarbon, the Hamiltonian matrix H = [ H i j ] {\displaystyle...

quantization rule, allowing the matrix elements of P and X for an arbitrary system to be determined simply from the form of the Hamiltonian. The new quantization...

way that quaternion addition and multiplication correspond to matrix addition and matrix multiplication. One is to use 2 × 2 complex matrices, and the...

physics, Hamiltonian mechanics is a reformulation of Lagrangian mechanics that emerged in 1833. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics...

the value of a linear operator (especially a modified Hamiltonian) in quantum theory Matrix coefficient, a type of function in representation theory...

A Hamiltonian system is a dynamical system governed by Hamilton's equations. In physics, this dynamical system describes the evolution of a physical system...

|\Gamma _{n}\rangle } can be found from direct diagonalization of Hamiltonian matrix containing crystal field and spin–orbit interactions. Taking into...

Branch cuts of the S-matrix in the complex-energy plane are associated to the opening of a scattering channel. In the Hamiltonian approach to quantum field...

Hamiltonian matrix — a matrix used in a variety of fields, including quantum mechanics and linear-quadratic regulator (LQR) systems. Irregular matrix...

high-field-seeking state). Assuming the magnetic-field dependence is linear, the Hamiltonian matrix for the system with the field applied can be written H = ( μ B ( t...

boundary conditions. Another approach is numerical matrix diagonalization. If the Hamiltonian matrix is computed in any complete basis, eigenvalues and...

graph theory Hamiltonian cycle, a special case of a Hamiltonian path Hamiltonian group, in group theory Hamiltonian matrix Hamiltonian numbers (or quaternions)...

eigendecomposition of a larger system. For the CARE, we define the Hamiltonian matrix Z = ( A − B R − 1 B ⊤ − Q − A ⊤ ) {\displaystyle Z={\begin{pmatrix}A&-BR^{-1}B^{\top...

matrix, a square matrix whose entries are either +1 or −1 and whose rows are mutually orthogonal Hamiltonian matrix, a 2n × 2n matrix A such that JA is...

the number of Hamiltonian cycles to a simpler counting problem, of counting cycle covers, which can be solved by computing certain matrix determinants...

{\displaystyle r} , the more accurate the simulation. If the Hamiltonian is represented as a Sparse matrix, the distributed edge coloring algorithm can be used...

mathematician Joseph Liouville, is a key theorem in classical statistical and Hamiltonian mechanics. It asserts that the phase-space distribution function is constant...