Bibliographic Details
| Title: |
A shortcut to the eigenvalues of the harmonic oscillator and the hydrogen atom. |
| Authors: |
Zhang, J. M.1,2 (AUTHOR) wdlang06@gmail.com, Lin, R. K.2,3 (AUTHOR) linrongkang413@gmail.com |
| Source: |
American Journal of Physics. Jul2026, Vol. 94 Issue 7, p582-584. 3p. |
| Subjects: |
Eigenvalues, Harmonic oscillators, Hydrogen atom, Energy levels (Quantum mechanics), Differential operators, Quantum mechanics, Wave functions |
| Abstract: |
Textbook solutions for the harmonic oscillator and the hydrogen atom using the Sommerfeld polynomial method often appear tedious and formidable to students. However, the differential operators acting on the reduced wave functions possess a convenient algebraic property: they preserve the subspace of polynomials of degree at most k. This observation makes the derivation of energy eigenvalues transparent and direct, without the need for the full power series recurrence relations. Editor's Note: This Note will delight quantum mechanics instructors, as it points out a simple way to derive the eigenstates and energies of the harmonic oscillator and hydrogen atom potentials. Do not miss it! [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
