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On matrices whose eigenvalues are in arithmetic progression

Published online by Cambridge University Press:  24 October 2008

P. T. Landsberg
P. T. Landsberg
Affiliation:
Department of Natural PhilosophyThe UniversityAberdeen
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Extract

The following matrix problems are well known in quantum mechanics:

(a) The one-dimensional harmonic oscillator. Given

determine the eigenvalues hjj of H, and the matrix elements of X, P if H is diagonal. It is found (Wigner (4)) that

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 47 , Issue 3 , July 1951 , pp. 585 - 590
Copyright
Copyright © Cambridge Philosophical Society 1951

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References

REFERENCES

(1)Dirac, P. A. M.Principles of quantum mechanics, 3rd ed. (Oxford, 1947).Google Scholar
(2)Landsberg, P. T.Phil. Mag. 39 (1948), 1001.CrossRefGoogle Scholar
(3)Schweber, S.Phys. Rev. 78 (1950), 613.CrossRefGoogle Scholar
(4)Wigner, E. P.Phys. Rev. 77 (1950), 711.CrossRefGoogle Scholar