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Rohin
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The paper I'm referring to can be accessed here: http://users.mat.unimi.it/users/galgani/arch/heis25ajp.pdf
On page 12, Werner Heisenberg, in the process of 're-interpreting atomic dynamics' from the principles of quantum theory, says that the Bohr Sommerfeld Quantization Rule, which says that the action integral of a period system over a closed region in the phase space is quantized and is equal to Planck's constant times a positive integer, appears arbitrary from the perspective of Bohr's Correspondence Principle?
Specifically, the equation he is referring to is equation (12) in the paper: loop_integral{pdq} = loop_integral{(x_dot)^2dt} = J(=nh), where n is an integer.
All I know is that the Correspondence Principle says that quantum systems in the limit of large quantum numbers should start emulating classical systems. I can't see how this points to a contradiction or an arbitrariness in the above quantization principle which Heisenberg seems to allude to in his paper. Could someone clarify this?
Thank you very much!
On page 12, Werner Heisenberg, in the process of 're-interpreting atomic dynamics' from the principles of quantum theory, says that the Bohr Sommerfeld Quantization Rule, which says that the action integral of a period system over a closed region in the phase space is quantized and is equal to Planck's constant times a positive integer, appears arbitrary from the perspective of Bohr's Correspondence Principle?
Specifically, the equation he is referring to is equation (12) in the paper: loop_integral{pdq} = loop_integral{(x_dot)^2dt} = J(=nh), where n is an integer.
All I know is that the Correspondence Principle says that quantum systems in the limit of large quantum numbers should start emulating classical systems. I can't see how this points to a contradiction or an arbitrariness in the above quantization principle which Heisenberg seems to allude to in his paper. Could someone clarify this?
Thank you very much!