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Benedict Irwin added Quantum.tex
over 9 years ago
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\section{Quantum Idea}
A quick thought was to use this idea for some physical (if you believe it) integral...
Weird recursive statements, for example. If we have a total energy, which is the sum of discreet energies, but we don't know what energies they are, we know the maximum energy is the largest, and the largest an energy could be, if there was only one, is the total...
(Rewrite)
We have at least one energy level.
The energy is the sum of all levels.
Close packed we use an integral.
If there was one level, the level would have an energy value equal to the total energy.
Therefore search in the range $0$ to $E$.
Assume we have a Quantum Harmonic Oscillator (QHO), we could try saying, \begin{equation}
E=\int_0^E \hbar \omega( E_n + \frac{1}{2} ) \; \mathrm{dE_n}
\end{equation}
Then $\hbar\omega$ becomes an $r$ like parameter, that is, at higher frequencies (more energy) there appear more splittings (levels). Why? Not sure, particle creation/annihilation?
