Timeline for Half-integer eigenvalues of orbital angular momentum
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 23, 2021 at 19:48 | comment | added | Ruslan | Integer $\ell$ has no significance in convergence of solutions of the radial equation. It only appears in the term $\propto -\frac{\ell(\ell+1)}{r^2}$ in the Hamiltonian, which is basically a (repulsive) centrifugal potential. Granted, the eigenvalues will change with non-integer $\ell$, and the Laguerre functions won't be polynomials, but the bounded solutions will still exist with different eigenvalues. What will indeed break down is the angular part, which will diverge at the poles due to the properties of the associated Legendre functions. | |
| Aug 26, 2019 at 15:19 | history | edited | Bill N | CC BY-SA 4.0 |
change convergent angular solutions to convergent radial solutions.
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| Aug 26, 2019 at 15:11 | comment | added | Bill N | The parameter $\ell$ is a partial differential equation separation parameter for the SWE. It appears in both the radial and angular parts. The solutions to the radial equation will diverge $r \to \infty$ if $\ell$ is non-integer. Take a look at Laguerre functions and/or Arfken's Mathematical Physics section on the Schoedinger Wave Equation (SWE). Maybe I should clarify my answer to say the radial solution diverges. | |
| Apr 10, 2018 at 20:28 | comment | added | DanielC | I do not see the divergence of the solution. Can you explain? | |
| Jan 14, 2015 at 18:55 | history | answered | Bill N | CC BY-SA 3.0 |