Search NASA⌕ Search

SEARCH · Search NASA

Results for “EIGENVALUE”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

The Eigenvector-Eigenvalue Identity and other pragmatic topics in linear algebra for physicists

Diagonalization of an Hermitian matrix is a common task in physics. All of us have diagonalized 2x2 matrices but few have diagonalized a 3x3 matrix algebraically except in special simplifying cases. In this colloquium, I will discuss the mathematics and methods for diagonalizing small, but larger than 2x2 marices, and discuss the recently rediscovered Eigenvector-Eigenvalue identity. As an explicit, pragmatic example I will use the propagation of neutrino's propagating through matter which is inherently a 3x3 problem.

Parke, Stephen [Fermilab] (ORCID:0000000320286782)↗
NASA NTRS1965

Studies in Perturbation Theory. XI. Lower Bounds to Energy Eigenvalues, Ground State, and Excited States

The bracketing theorem in the partitioning technique for solving the Schrödinger equation may be used in principle to determine upper and lower bounds to energy eigenvalues. Practical lower bounds of any accuracy desired may be evaluated by utilizing the properties of ``inner projections'' on finite manifolds in the Hilbert space. The method is here applied to the ground state and excited states of a Hamiltonian H=H(sub 0)+V having a positive definite perturbation V. Even if inspiration is derived from the method of intermediate Hamiltonians, the final results are of bracketing type and independent of this approach. The method is numerically illustrated in some accompanying papers.

Loewdin, Per-Olov↗
NASA NTRS1965

Lower Bounds to Energy Eigenvalues for the Stark Effect in a Rigid Rotator

Upper and lower bounds have been calculated for the energy levels of a rigid rotator in an electric field, in order to study the problems associated with the use of the partitioning method for bracketing an eigenvalue of the Schrödinger equation. Results of arbitrarily high accuracy are possible in this example.

Choi, Jong H.↗