1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Re-examining the value of old quantization and the Bohr atom approach
Rent:
Rent this article for
USD
10.1119/1.4769785
/content/aapt/journal/ajp/81/2/10.1119/1.4769785
http://aip.metastore.ingenta.com/content/aapt/journal/ajp/81/2/10.1119/1.4769785

Figures

Image of Fig. 1.
Fig. 1.

The limit of classical orbits approaching for the Coulomb potential (left), the SHO potential (center), and the ISW potential (right). The parameter captures the number of times a path between the maximum radius and the center is traversed in the limit ; for the Coulomb potential this is , for the other two it is .

Image of Fig. 2.
Fig. 2.

The numerical energy spectrum of the logarithmic potential plotted with the old quantization spectrum from Eq. (23) . The residual differences between the two are shown in the inset.

Image of Fig. 3.
Fig. 3.

The first 50 critical values , plotted with the prediction using old quantization from Eq. (29) . The residual differences between the two are shown in the inset.

Tables

Generic image for table
Table I.

The first 20 numerically calculated energy eigenvalues for spherically-symmetric states in the logarithmic potential, along with the first 20 old-quantization energy values. Numerical errors are on the order of , which is generally much smaller than the discrepancy between the numerical eigenvalue and the old-quantization eigenvalue.

Generic image for table
Table II.

The first 20 numerically calculated critical values , together with the old-quantization values. Numerical errors range from to and are in general much smaller than the discrepancy between old-quantization and numerical values.

Loading

Article metrics loading...

/content/aapt/journal/ajp/81/2/10.1119/1.4769785
2013-01-22
2014-04-17
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Re-examining the value of old quantization and the Bohr atom approach
http://aip.metastore.ingenta.com/content/aapt/journal/ajp/81/2/10.1119/1.4769785
10.1119/1.4769785
SEARCH_EXPAND_ITEM