Explicit representations of Pollaczek polynomials corresponding to an exactly solvable discretisation of hydrogen radial Schrödinger equation

Details Explicit representations of Pollaczek polynomials corresponding to an exactly solvable discretisation of hydrogen radial Schrödinger equation Explicit representations of Pollaczek polynomials corresponding to an exactly solvable discretisation of hydrogen radial Schrödinger equation

2004-07-21

arxiv.org/abs/math-ph/0407044v2

J. Phys. A: Math. Gen. 38 1279-1285 (2005)

Physics

Mathematical Physics

7 pages, no figures, revised version, some minor errors corrected

Scientific paper

10.1088/0305-4470/38/6/007

We consider an exactly solvable discretisation of the radial Schr\"odinger equation of the hydrogen atom with l=0. We first examine direct solutions of the finite difference equation and remark that the solutions can be analytically continued entire functions. A recursive expression for the coefficients in the solution is obtained. The next step is to identify the related three-term recursion relation for Pollaczek polynomials. One-to-one correspondence between the spectral and position representations facilitates the evaluation of Pollaczek polynomials corresponding to the discrete spectrum. Finally, we obtain two alternative and explicit expressions for the solutions of the original difference equation.

Affiliated with

Also associated with

No associations

Rating

Explicit representations of Pollaczek polynomials corresponding to an exactly solvable discretisation of hydrogen radial Schrödinger equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Explicit representations of Pollaczek polynomials corresponding to an exactly solvable discretisation of hydrogen radial Schrödinger equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Explicit representations of Pollaczek polynomials corresponding to an exactly solvable discretisation of hydrogen radial Schrödinger equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-1063