Abstract
The SO q (N)-invariant Schrödinger equation for the free particle is formulated in polar coordinates as a partial differential equation in noncommutative geometry. For each value of the total angular momentum, a Hilbert space of radial functions is constructed as the space of normalizable functions respective to the q-integral. The spectrum of the Hamiltonian is found to be discrete.
Similar content being viewed by others
References
Wess, J., Talk given in ‘300-Jahrfeier der Mathematischen Gesellschaft in Hamburg’, 1990.
Carow-Watamura, U., Schlieker, M., and Watamura, S., Z. Phys. C. 49, 439 (1991).
Fiore, G., Preprint SISSA 35/92/EP, 1992.
Fiore, G., Forthcoming paper.
Weich, W., PhD Thesis, Karlsruhe University, 1990.
Woronowicz, S. L., Comm. Math. Phys. 122, 613 1989.
Carow-Watamura, U., Schlieker, M., Watamura, S., and Weich, W., Comm. Math. Phys. 142, 605 (1991).
Ogievetsky, O., Preprint MPI-Ph/91-103, 1991.
Ogievetsky, O., and Zumino, B., Reality in the differential calculus on q-Euclidean spaces, Lctt. Math. Phys. 25, 121–130 (1992).
Schwenk, J. and Wess, J., preprint MPI-Ph/92-8, 1992.
Woronowicz, S. L., Invent. Math. 93, 35 (1988).
Carow-Watamura, U., Schlieker, M., Scholl, M., and Watamura, S. Z. Phys. C 48, 159 (1990).
Jackson, F. H., Quart. J. Math. Oxford Ser. (2) 1 (1951).
Reshetikhin, N. Yu., LOMI preprint E-4-87, 1987.