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Kyle Kanos
Kyle Kanos
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Here's a very basic way to see this easily: this

This is Action, search for the "Abbreviated Action": http://en.wikipedia.org/wiki/Action_(physics)search for the "Abbreviated Action", and it has the SI unit of Joule-second. This is the equation that Planck (and later, Einstein) used: "E=nhf" $$E=nhf$$ for (n=1,2,3...$n=1,2,3...$ and f$f$ in frequency, in unit of 1/second). This

This means that the Planck's constant has also an unit of Joule-second, therefore, you can interpret "nh"$nh$ as the Action of the system (since "n"$n$ is dimensionless, it will maintain the unit, and it is only used to give the "correct" answer, since not every mechanical system has "h"$h$ as the Action, "n"$n$ should be used).

So So "nh=integral(p)dq", which$$nh=\int p\,dq$$ which is the Sommerfield rule for quantization. This is just an intuition of how it works.

Here's a very basic way to see this easily: this is Action, search for the "Abbreviated Action": http://en.wikipedia.org/wiki/Action_(physics), and it has the SI unit of Joule-second. This is the equation that Planck (and later, Einstein) used: "E=nhf" (n=1,2,3... and f in frequency, in unit of 1/second). This means that the Planck's constant has also an unit of Joule-second, therefore, you can interpret "nh" as the Action of the system (since "n" is dimensionless, it will maintain the unit, and it is only used to give the "correct" answer, since not every mechanical system has "h" as the Action, "n" should be used). So "nh=integral(p)dq", which is the Sommerfield rule for quantization. This is just an intuition of how it works.

Here's a very basic way to see this easily:

This is Action, search for the "Abbreviated Action", and it has the SI unit of Joule-second. This is the equation that Planck (and later, Einstein) used: $$E=nhf$$ for $n=1,2,3...$ and $f$ in frequency, in unit of 1/second).

This means that the Planck's constant has also an unit of Joule-second, therefore, you can interpret $nh$ as the Action of the system (since $n$ is dimensionless, it will maintain the unit, and it is only used to give the "correct" answer, since not every mechanical system has $h$ as the Action, $n$ should be used).

So $$nh=\int p\,dq$$ which is the Sommerfield rule for quantization. This is just an intuition of how it works.

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farofus
farofus
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Here's a very basic way to see this easily: this is Action, search for the "Abbreviated Action": http://en.wikipedia.org/wiki/Action_(physics), and it has the SI unit of Joule-second. This is the equation that Planck (and later, Einstein) used: "E=nhf" (n=1,2,3... and f in frequency, in unit of 1/second). This means that the Planck's constant has also an unit of Joule-second, therefore, you can interpret "nh" as the Action of the system (since "n" is dimensionless, it will maintain the unit, and it is only used to give the "correct" answer, since not every mechanical system has "h" as the Action, "n" should be used). So "nh=integral(p)dq", which is the Sommerfield rule for quantization. This is just an intuition of how it works.