Series-termination quantization of the Coulomb radial equation

For a radial solution regular at the origin, writing

R = e^{- γ r} \sum_{n \geq 0} a_{n} r^{n}

gives

a_{n} = \frac{2 γn - β}{n ( n + 1 )} a_{n - 1} .

Normalizability at infinity forces the series to terminate, so

2 γ N = β

for a positive integer

N

and

E_{N} = - m q^{4} / (2 ℏ^{2} N^{2})

.

Table of contents
- Hydrogen ground-state energy Series-termination quantization of the Coulomb radial equation

Hydrogen ground-state energy

The lowest Coulomb bound-state energy is

E_{1} = - \frac{m q ^{4}}{2 ℏ ^{2}} .

 Ancestors (5)

 Incoming links (2)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version