# I Planck's constant and quantization of energy

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1. Sep 25, 2016

### redtree

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?

Last edited: Sep 25, 2016
2. Sep 25, 2016

### Staff: Mentor

Right. For bound states it is.
You can work in units where it is equal to 1. Yes, it is just a unit conversion - but the fact that this conversion is possible is not trivial.

3. Sep 25, 2016

### Staff: Mentor

It doesn't. Quantization of energy appears when you solve Schrodinger's equation for bound states. The simplest example is the one-dimensional infinite square well; in the solutions to Schrodinger's equation for that potential $k$ can only take on discrete values.

4. Sep 26, 2016

### vanhees71

...and please don't use the awful $\mathrm{i} c t$ convention of the SRT pseudometric. Particularly when it comes to QFT, with that you'll confuse yourself even more than the subject itself can ever do when done in the real-time formalism ;-).