- #1

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Given:

##\textbf{E}=\hbar \textbf{k}##

where ##\textbf{k} = [\vec{k}_1, \vec{k}_2,\vec{k}_3, i c \omega]##

If ##\textbf{k}## can vary continuously, how does the equation imply that energy is quantized?

For example, ##y = m x +b## where ##m = \hbar## does not imply quantized ##y##.

For ##\textbf{E}## to be quantized mustn't ##\textbf{k}## be quantized?

And why should ##\hbar## be considered anything other than a unit conversion?

##\textbf{E}=\hbar \textbf{k}##

where ##\textbf{k} = [\vec{k}_1, \vec{k}_2,\vec{k}_3, i c \omega]##

If ##\textbf{k}## can vary continuously, how does the equation imply that energy is quantized?

For example, ##y = m x +b## where ##m = \hbar## does not imply quantized ##y##.

For ##\textbf{E}## to be quantized mustn't ##\textbf{k}## be quantized?

And why should ##\hbar## be considered anything other than a unit conversion?

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