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One-Dimensional Model Problems

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Part of the book series: Springer Advanced Texts in Chemistry ((SATC))

Abstract

In the previous chapter, the basic ideas of quantum mechanics were introduced by means of several postulates. It was also seen that there are several possible equivalent ways of viewing quantum mechanics, commonly referred to as the Schrödinger picture, the Heisenberg picture, and the interaction picture. Since these are all equivalent views of the same phenomena, the choice of which one to employ when attempting to solve a problem of interest can be made on the basis of which one is most convenient to use.

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References

  1. L. I. Schiff, Quantum Mechanics, McGraw-Hill, New York, 1968, Chapter 6.

    Google Scholar 

  2. H. S. Green, Matrix Methods in Quantum Mechanics, Barnes & Noble, New York, 1965.

    Google Scholar 

  3. J. C. Slater, Phys. Rev., 51, 846 (1937)

    Article  CAS  Google Scholar 

  4. H. S. Silverstone, Phys. Rev. (A), 5, 1092 (1972).

    Article  Google Scholar 

  5. G. G. Hall, J. Hyslop, and D. Rees, Int. J. Quantum Chem., 3, 195 (1969).

    Article  CAS  Google Scholar 

  6. G. Hellwig, Differential Operators of Mathematical Physics, Addison-Wesley, Reading, MA, 1967, pp. 39-49 for a discussion of these conditions.

    Google Scholar 

  7. Also, see R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. 1, Interscience Publishers, New York, 1961, pp. 293 - 294.

    Google Scholar 

  8. R. Loudon, Am. J. Phys., 27, 649 (1959).

    Article  CAS  Google Scholar 

  9. G. Hellwig, Differential Operators of Mathematical Physics, Addison-Wesley, Reading, MA, 1967, pp. 3949.

    Google Scholar 

  10. L. Pauling, J. Chem. Phys., 4, 673 (1936), and Problem 5-5.

    Google Scholar 

  11. W. Kaplan, Ordinary Differential Equations, Addison-Wesley, Reading, MA, 1961, Chapter 4.

    Google Scholar 

  12. J. R. Platt, K. Ruedenberg, C. W. Scherr, N. S. Ham, H. Labhart, and W. Licten, Free Electron Theory of Conjugated Molecules, John Wiley, New York, 1964.

    Google Scholar 

  13. J. C. Slater, Quantum Theory of Molecules and Solids, Vol. 3, McGraw-Hill, New York, 1967, p. 9.

    Google Scholar 

  14. R. Fowler and E. A. Guggenheim, Statistical Thermodynamics, Cambridge University Press, Cambridge, 1952, p. 72.

    Google Scholar 

  15. D. Bohm, Quantum Theory, Prentice-Hall, Englewood Cliffs, NJ, 1957, pp. 247 - 251

    Google Scholar 

  16. P. A. Deutchman, Am. J. Phys., 39, 952 (1971).

    Article  Google Scholar 

  17. C. C. Costain, Phys. Rev., 82, 108 (1951).

    Article  CAS  Google Scholar 

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© 1989 Springer-Verlag New York Inc.

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Christoffersen, R.E. (1989). One-Dimensional Model Problems. In: Basic Principles and Techniques of Molecular Quantum Mechanics. Springer Advanced Texts in Chemistry. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-6360-6_5

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  • DOI: https://doi.org/10.1007/978-1-4684-6360-6_5

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4684-6362-0

  • Online ISBN: 978-1-4684-6360-6

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