# Solving Hydrogen Atom Problem Using Spherical Polar Coordinates: A Qualitative Study

### Abstract

Quantum mechanics has completed century since its genesis. Quantum mechanics is taught at various levels-starting from school and colleges to universities. Regression methods are introduced at under graduate and post graduate levels to solve Schrodinger equation for finding solutions of various trivial and non-trivial physical problems. The common problems, which students encounter at UG level are- particle in a box, potential step and barriers, harmonic oscillator and hydrogen atom. It has been observed that students lack clarity in solving and grasping the hydrogen atom problem. Two reasons can be accounted for this. It is perhaps a lengthy derivation and students, many times, are not well acquainted with the requisite knowledge of Spherical Polar Co-ordinate system. In this article, a brief review on the birth of quantum mechanics is presented judiciously discussing the contribution of Schrodinger, before solving the hydrogen atom problem. Readers are first introduced to spherical-polar coordinate system. The radial solutions, radial probability distribution functions, and hydrogen orbital, are plotted using Mathematica software v.12, for the sake of visualization and understanding.### References

Alain, A. and Villain, J. (2017), The birth of wave mechanics (1923-1926), Comptes Rendus Physique, 18, 583-585.

Heisenberg, W. (1925), Über quantentheoretische Umdeutungkinematischer und mechanischer Beziehungen, Z. Phys. 33, 879.

Born, M. & Jordan, P. (1925), Zur Quantenmechanik, Z. Phys. 34, 858.

Aschman, D. &Keaney, B. (1989), The Legacy of Erwin Schrodinegr: Quantum Mechanics,Trans Roy. Soc. S. Africa, Part-I, 47, 81-101.

Reiter, W. L. &Yngvason, J. (2013), Erwin Schrodinger- 50 Years After, ESI Lectures in Mathematics and Physics, EuroepanMathemtical Society Publishing House.

Fedak, W. A. & Jeffrey, J. P. (2009), The 1925 Born and Jordan Paper “On Quantum Mechanics”, American Journal of Physics,77, 128.

Ghatak, A. & Loknathan, S. (2014), Qunatum Mechanics: Theory and Application (5th Ed.), Macmillan India.

Schiff, L. I. & Bandhyopadhyay, J. (2017), Quantum Mechanics (4th Ed.), McGraw Hill Education, India.

Fenyman, R., The Feynman Lectures on Physics, Volume III (1st Ed.), Pearson Education.

Retrieved from -http://www.astro.caltech.edu/~srk/Ay126/Lectures/Lecture3/SchrodingerModel.pdf,(Chapter-10 The Hydrogen Atom).

Wolfram, S. (1996), The Mathematica Book (3r. Ed.), Cambridge University Press, USA.

Heisenberg, W. (1925), Über quantentheoretische Umdeutungkinematischer und mechanischer Beziehungen, Z. Phys. 33, 879.

Born, M. & Jordan, P. (1925), Zur Quantenmechanik, Z. Phys. 34, 858.

Aschman, D. &Keaney, B. (1989), The Legacy of Erwin Schrodinegr: Quantum Mechanics,Trans Roy. Soc. S. Africa, Part-I, 47, 81-101.

Reiter, W. L. &Yngvason, J. (2013), Erwin Schrodinger- 50 Years After, ESI Lectures in Mathematics and Physics, EuroepanMathemtical Society Publishing House.

Fedak, W. A. & Jeffrey, J. P. (2009), The 1925 Born and Jordan Paper “On Quantum Mechanics”, American Journal of Physics,77, 128.

Ghatak, A. & Loknathan, S. (2014), Qunatum Mechanics: Theory and Application (5th Ed.), Macmillan India.

Schiff, L. I. & Bandhyopadhyay, J. (2017), Quantum Mechanics (4th Ed.), McGraw Hill Education, India.

Fenyman, R., The Feynman Lectures on Physics, Volume III (1st Ed.), Pearson Education.

Retrieved from -http://www.astro.caltech.edu/~srk/Ay126/Lectures/Lecture3/SchrodingerModel.pdf,(Chapter-10 The Hydrogen Atom).

Wolfram, S. (1996), The Mathematica Book (3r. Ed.), Cambridge University Press, USA.

Published

2019-09-05

How to Cite

SINGH, Satya Pal.
Solving Hydrogen Atom Problem Using Spherical Polar Coordinates: A Qualitative Study.

**European Journal of Physics Education**, [S.l.], v. 10, n. 4, p. 1-21, sep. 2019. ISSN 1309-7202. Available at: <http://eu-journal.org/index.php/EJPE/article/view/247>. Date accessed: 23 oct. 2019. doi: https://doi.org/10.20308/ejpe.v10i4.247.
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Classroom Physics

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