Kravchuk polynomials and irreducible representations of the rotation group \(\mathrm{SO}(3)\). (English) Zbl 1312.33050
Summary: We set forth that the Kravchuk polynomials of a discrete variable are actually “encoded” within appropriate finite-dimensional irreducible representations of the group of rotations of three-dimensional space \(\mathrm{SO}(3)\). Hence, discrete irreducible representation spaces of the group \(\mathrm{SO}(3)\) can be naturally interpreted as finite (discrete) versions of the linear quantum harmonic oscillator.
MSC:
| 33D45 | Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) |
| 39A70 | Difference operators |
| 47B39 | Linear difference operators |
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