The Coulomb potential in quantum mechanics revisited

@article{Othman2016TheCP,
  title={The Coulomb potential in quantum mechanics revisited},
  author={Anas Othman and Marc de Montigny and Frank Marsiglio},
  journal={American Journal of Physics},
  year={2016},
  volume={85},
  pages={346-351}
}
The procedure commonly used in textbooks for determining the eigenvalues and eigenstates for a particle in an attractive Coulomb potential is not symmetric in the way the boundary conditions at r = 0 and r → ∞ are considered. We highlight this fact by solving a model for the Coulomb potential with a cutoff (representing the finite extent of the nucleus). In the limit that the cutoff is reduced to zero, we recover the standard result, albeit in a non-standard way. This example is used to… 
3 Citations

Figures from this paper

Acceleration in quantum mechanics and electric charge quantization

In this study, we have discussed the implications of acceleration in quantum mechanics by means of a generalized derivative operator (GDO). A new Schrödinger equation is obtained which depends on the

A physicist's guide to the solution of Kummer's equation and confluent hypergeometric functions

The confluent hypergeometric equation, also known as Kummer's equation, is one of the most important differential equations in physics, chemistry, and engineering. Its two power series solutions are

The bound-state solutions of the one-dimensional hydrogen atom

The one-dimensional hydrogen atom is an intriguing quantum mechanics problem that exhibits several properties which have been continually debated. In particular, there has been variance as to whether

References

SHOWING 1-2 OF 2 REFERENCES

Quantisation as a Problem of Proper Values (Part I)

  • 1928