One-Dimensional Model Problems
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.
KeywordsEnergy Level Harmonic Oscillator Matrix Representation Uncertainty Principle Hermite Polynomial
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- 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
- 5.G. Hellwig, Differential Operators of Mathematical Physics, Addison-Wesley, Reading, MA, 1967, pp. 39-49 for a discussion of these conditions.Google Scholar
- 6.Also, see R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. 1, Interscience Publishers, New York, 1961, pp. 293 - 294.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
- 13.W. Kaplan, Ordinary Differential Equations, Addison-Wesley, Reading, MA, 1961, Chapter 4.Google Scholar
- 19.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
- 20.J. C. Slater, Quantum Theory of Molecules and Solids, Vol. 3, McGraw-Hill, New York, 1967, p. 9.Google Scholar
- 21.R. Fowler and E. A. Guggenheim, Statistical Thermodynamics, Cambridge University Press, Cambridge, 1952, p. 72.Google Scholar
- 23.D. Bohm, Quantum Theory, Prentice-Hall, Englewood Cliffs, NJ, 1957, pp. 247 - 251Google Scholar