Full text loading...
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Self-adjoint extensions of operators and the teaching of quantum mechanics
1.L. E. Ballentine, Quantum Mechanics (Prentice–Hall, Englewood Cliffs, NJ, 1990).
2.A. Z. Capri, “Self-adjointness and spontaneously broken symmetry,” Am. J. Phys. 45, 823–825 (1977).
3.A. Cabo, J. L. Lucio, and H. Mercado, “On scale invariance and anomalies in quantum mechanics,” Am. J. Phys. 66, 240–246 (1998).
4.R. Jackiw, “Delta function potentials in two and three dimensional quantum mechanics,” in M. A. Bég Memorial Volume, edited by A. Ali and P. Hoodbhoy (World Scientific, Singapore, 1991), pp. 1–16.
5.N. I. Akhiezer and I. M. Glazman, Theory of Linear Operators in Hilbert Space (Ungar, New York, 1961).
6.M. A. Naimark, Linear Differential Operators (Ungar, New York, 1968), Vol. 2.
7.J. M. Lévy-Leblond and F. Balibar, Quantics (North-Holland, Amsterdam, 1990).
8.W. Greiner, Quantum Mechanics (Springer-Verlag, Berlin, 1989).
9.Notice that the positive function (4) is nearly equal to the eigenfunction as
10.H. Weyl, Math. Ann. 68, 220–269 (1910).
11.J. von Neumann, Math. Ann. 102, 49–131 (1929).
12.C. Cohen-Tannoudji, B. Diu, and F. Laloë, Quantum Mechanics (Wiley, New York, 1977).
13.L. Schiff, Quantum Mechanics (McGraw–Hill, New York, 1965), 3rd ed.
14.An extended version, with mathematical details, is available from the preprint PAR/LPTHE/99-43.
15.H. B. Rosentock, “Specific heat of a particle in a box,” Am. J. Phys. 30, 38–40 (1962).
16.V. Granados and N. Aquino, “Comment on specific heat revisited,” Am. J. Phys. 67, 450–451 (1999).
17.D. H. Berman, “Boundary effects in quantum mechanics,” Am. J. Phys. 59, 937–941 (1991).
18.To make things simple we say that a function is absolutely continuous for if it can be written in the form where is absolutely integrable for any Absolute continuity in a finite interval implies uniform continuity, whereas the converse is not true. The interested reader is referred to Ref. 19, p. 337.
19.A. Kolmogorov and S. Fomine, Eléments de la Théorie des Fonctions et de L’analyse Fonctionnelle (Mir-Ellipses, Paris, 1994).
Article metrics loading...