Question

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What is Bohr's correspondence principle ? ​

Answer 1

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☕ Among current Bohr scholars there is a consensus that Bohr did not intend his correspondence principle to designate some sort of general requirement that quantum mechanics recover the predictions of classical mechanics in the classical limit . There is far less agreement, however, concerning precisely which relation between classical and quantum mechanics Bohr intended to designate by the correspondence principle. There are three prominent contenders in the literature, all of which find support in Bohr’s writings. These three interpretations can be labeled: the frequency interpretation, the intensity interpretation, and the selection rule interpretation .

☕ According to the frequency interpretation, the correspondence principle is defined as a statistical asymptotic agreement between the (quantum) frequency, $\bf{\nu_{n'\:\rightarrow\:n''}}$, of radiation emitted in a quantum jump of difference τ from state n' to n'' and the (classical) frequency $\bf{(\omega_{\tau})}$ in the $\sf{\tau^{th}}$ harmonic of the classical motion in the n' stationary state, namely

✔️ $\bf\purple{\nu_{n'\:\rightarrow\:n''}\:=\:\omega_{\tau}\:=\:\tau\:\omega\:,\:for\:large\:n\:}$

Where,

• n' - n'' = τ

Answer 2

According to the selection rule interpretation, Bohr's correspondence principle is best understood as the statement that each allowed quantum transition between stationary states corresponds to one harmonic component of the classical motion.