Generalized correspondence principle for the Bohr atom.---It is shown that when an electron spirals in from an orbit of quantum number ${n}_{2}$ to an orbit of quantum number ${n}_{1}$ , the frequency of the radiation emitted is equal to an integer (${n}_{2}\ensuremath{-}{n}_{1}$) times the mean frequency of rotations in its orbit during the spiraling, assuming that the number of rotations made for a change of quantum level $\mathrm{dn}$ is proportional to $\mathrm{dn}$ . That is, the mean is defined as the ratio to (${n}_{2}\ensuremath{-}{n}_{1}$) of the integral from ${n}_{1}$ to ${n}_{2}$ of ${\ensuremath{\nu}}_{\mathrm{c}} \mathrm{dn}$ where ${\ensuremath{\nu}}_{c}$ is the classical frequency of rotation corresponding to any value of $n$ . No explanation is offered as to why radiation begins and stops at integral values of $n$ , nor why the radiation emitted in the manner assumed is monochromatic.Generalized correspondence principle for the Bohr atom.---It is shown that when an electron spirals in from an orbit of quantum number ${n}_{2}$ to an orbit of quantum number ${n}_{1}$, the frequency of the radiation emitted is equal to an integer (${n}_{2}\ensuremath{-}{n}_{1}$) times the mean frequency of rotations in its orbit during the spiraling, assuming that the number of rotations made for a change of quantum level $\mathrm{dn}$ is proportional to $\mathrm{dn}$. That is, the mean is defined as the ratio to (${n}_{2}\ensuremath{-}{n}_{1}$) of the integral from ${n}_{1}$ to ${n}_{2}$ of ${\ensuremath{\nu}}_{\mathrm{c}} \mathrm{dn}$ where ${\ensuremath{\nu}}_{c}$ is the classical frequency of rotation corresponding to any value of $n$. No explanation is offered as to why radiation begins and stops at integral values of $n$, nor why the radiation emitted in the manner assumed is monochromatic.

Physical ReviewNov 1, 19242 citations

The correspondence principle between classical and quantum quantities

Yu.I. Zaparovannyi

Russian Physics JournalJun 1, 19740 citations

Generalized correspondence principle for the Bohr atom.---It is shown that when an electron spirals in from an orbit of quantum number

{n}_{2}

to an orbit of quantum number

{n}_{1}

, the frequency of the radiation emitted is equal to an integer (${n}_{2}\ensuremath{-}{n}_{1}$) times the mean frequency of rotations in its orbit during the spiraling, assuming that the number of rotations made for a change of quantum level

\mathrm{dn}

is proportional to

\mathrm{dn}

. That is, the mean is defined as the ratio to (${n}_{2}\ensuremath{-}{n}_{1}$) of the integral from

{n}_{1}

{n}_{2}

of ${\ensuremath{\nu}}_{\mathrm{c}} \mathrm{dn}$ where ${\ensuremath{\nu}}_{c}$ is the classical frequency of rotation corresponding to any value of

n

. No explanation is offered as to why radiation begins and stops at integral values of

n

, nor why the radiation emitted in the manner assumed is monochromatic.