# Planck's constant and quantization of energy

• I
• redtree
In summary, the conversation discusses the relationship between energy and the wave vector, where the wave vector can vary continuously. The equation does not imply that energy is quantized, but for bound states, the wave vector must be quantized for energy to be quantized. The value of ##\hbar## can be considered as a unit conversion, but its significance in quantizing energy is not trivial.
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:
redtree said:
For ##\textbf{E}## to be quantized mustn't ##\textbf{k}## be quantized?
Right. For bound states it is.
And why should ##\hbar## be considered anything other than a unit conversion?
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.

qnt200
redtree said:
If k\textbf{k} can vary continuously, how does the equation imply that energy is quantized?
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.

...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 ;-).

## 1. What is Planck's constant?

Planck's constant (denoted as h) is a fundamental constant in quantum mechanics that relates the energy of a single quantum of electromagnetic radiation to its frequency. It has a value of approximately 6.626 x 10^-34 joule seconds.

## 2. How did Planck's constant contribute to the development of quantum mechanics?

Planck's constant was first introduced in 1900 by German physicist Max Planck to explain the observed behavior of blackbody radiation. It later became a fundamental constant in quantum mechanics, playing a crucial role in the understanding of the quantization of energy and the behavior of particles at the atomic and subatomic level.

## 3. What is the significance of quantization of energy in relation to Planck's constant?

The quantization of energy refers to the idea that energy can only exist in discrete, specific amounts rather than being continuous. Planck's constant is the physical constant that relates the energy of a single quantum to its frequency, providing a mathematical basis for the quantization of energy.

## 4. How is Planck's constant used in practical applications?

Planck's constant is used in a wide range of practical applications, such as in the development of electronic devices like transistors and solar cells, and in the measurement of light and radiation. It is also used in the development of quantum technologies, including quantum computing and cryptography.

## 5. Has Planck's constant ever been challenged or revised?

No, Planck's constant has not been challenged or revised since its introduction in 1900. However, there have been efforts to more accurately measure its value, resulting in a slight adjustment to its numerical value over time. The most recent redefinition of the International System of Units in 2018 fixed the value of Planck's constant to be exactly 6.62607015 x 10^-34 joule seconds.

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