DOI: 10.1063/1.1701483. Studies in Perturbation Theory. XI. Lower Bounds to Energy Eigenvalues, Ground State, and Excited States

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

10.1063/1.1701483

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

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=H0+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.

Bibliography

LÃ¶wdin, P.-O. (1965). Studies in Perturbation Theory. XI. Lower Bounds to Energy Eigenvalues, Ground State, and Excited States. The Journal of Chemical Physics, 43(10), S175âS185.

Authors 1

Per-Olov Löwdin (first)

References 23 Referenced 133

10.1103/PhysRev.139.A357 / Phys. Rev. (1965)
{'key': '2024020715531067000_r2'}
{'key': '2024020715531067000_r3'}
10.1103/PhysRev.120.144 / Phys. Rev. (1960)
{'key': '2024020715531067000_r4a', 'first-page': '289', 'volume': '10', 'year': '1961', 'journal-title': 'J. Math. Mech.'} / J. Math. Mech. (1961)
{'key': '2024020715531067000_r4b', 'first-page': '105', 'volume': '65B', 'year': '1961', 'journal-title': 'J. Res. Natl. Bur. Std.'} / J. Res. Natl. Bur. Std. (1961)
10.1103/PhysRev.124.483 / Phys. Rev. (1961)
10.1063/1.1724246 / J. Math. Phys. (1962)
10.1007/BF00281201 / Arch. Rational Mech. Anal. (1962)
10.1063/1.1704045 / J. Math. Phys. (1963)
10.1103/RevModPhys.35.712 / Rev. Mod. Phys. (1963)
10.2140/pjm.1963.13.1229 / Pac. J. Math. (1963)
10.1007/BF00281233 / Arch. Rational Mech. and Anal. (1963)
10.1002/sapm196443115 / J. Math. and Phys. (1964)
10.1063/1.1724312 / J. Math. Phys. (1962)
10.1016/0022-2852(63)90151-6 / J. Mol. Spectry. (1963)
10.1016/0022-2852(64)90081-5 / J. Mol. Spectrosc. (1964)
10.1103/PhysRev.135.A1220 / Phys. Rev. (1964)
10.1063/1.1701482 / J. Chem. Phys. (1965)
{'key': '2024020715531067000_r8'}
10.1016/0022-2852(64)90107-9 / J. Mol. Spectry. (1964)
{'key': '2024020715531067000_r10', 'first-page': '1392', 'volume': '94', 'year': '1954', 'journal-title': 'Phys. Rev.'} / Phys. Rev. (1954)
10.1103/PhysRev.95.1167 / Phys. Rev. (1954)

Dates

Type	When
Created	20 years, 7 months ago (Jan. 9, 2005, 3:01 a.m.)
Deposited	1 year, 6 months ago (Feb. 7, 2024, 5:15 p.m.)
Indexed	1 year, 5 months ago (March 6, 2024, 2:42 a.m.)
Issued	59 years, 9 months ago (Nov. 15, 1965)
Published	59 years, 9 months ago (Nov. 15, 1965)
Published Print	59 years, 9 months ago (Nov. 15, 1965)

Funders 0

None

BibTeX

@article{L_wdin_1965, title={Studies in Perturbation Theory. XI. Lower Bounds to Energy Eigenvalues, Ground State, and Excited States}, volume={43}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.1701483}, DOI={10.1063/1.1701483}, number={10}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Löwdin, Per-Olov}, year={1965}, month=nov, pages={S175–S185} }

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