论文信息 - A Note on the Quantum‐Mechanical Perturbation Theory

A Note on the Quantum‐Mechanical Perturbation Theory

The solution of the quantum‐mechanical eigenvalue problem is discussed for cases when a series of approximate eigenfunctions is known. If these ``unperturbed'' states are divided into two classes, a perturbation formula is derived giving the influence of one class of states on the other in the final solution. The formula contains as special cases: (i) the Schrodinger‐Brillouin formula for the eigenvalue of a nondegenerate state, (ii) a new simple formula for treating a class of degenerate states, and (iii) the splitting of the secular equation in cases where the system naturally consists of two independent parts in mutual interaction.

Per-Olov Löwdin | P. Löwdin

[1] L. Brillouin. Les problèmes de perturbations et les champs self-consistents , 1932 .

[2] Frederick Albert Matsen IV. Molecular Orbital Theory and Spectra of Monosubstituted Benzenes. I. The Resonance Effect1 , 1950 .

[3] E. Gora. Quantentheorie der Strahlungsdämpfung , 1943 .

[4] K. Herzfeld. Electron levels in polyatomic molecules having resonating double bonds. , 1947, Chemical reviews.

[5] O. Jordahl. The Effect of Crystalline Electric Fields on the Paramagnetic Susceptibility of Cupric Salts , 1934 .

[6] A. Sklar. The Near Ultraviolet Absorption of Substituted Benzenes , 1939 .

[7] K. F. Niessen. On the Saturation of the Electric and Magnetic Polarization of Gases in Quantum Mechanics , 1929 .

[8] E. Feenberg. A Note on Perturbation Theory , 1948 .

[9] M. Dewar,et al. A modification of the molecular orbital method: the LCMO method , 1949, Mathematical Proceedings of the Cambridge Philosophical Society.