Quantization of Energy in Quantum Mechanics - Real Examples?

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Discussion Overview

The discussion revolves around the concept of energy quantization in quantum mechanics, exploring its origins, implications, and real-world examples. Participants inquire about the nature of quantization and seek concrete instances where this phenomenon is observed, particularly in atomic systems.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the reason behind the term "quantization of energy" in quantum mechanics and seeks real physical examples.
  • Another participant cites the energy of electrons in atomic orbitals as a concrete example of energy quantization.
  • A third participant introduces Planck's constant as a fundamental aspect of energy quantization, explaining that physical action must be a multiple of a small quantity, which contrasts with everyday experiences of continuous changes.
  • One participant reiterates the question about the occurrence of energy quantization and mentions that it is observed in atomic spectra, which display discrete spectral lines linked to specific energy differences, and notes the mathematical derivation via the Schrödinger equation.

Areas of Agreement / Disagreement

Participants present multiple viewpoints on the topic, with some agreeing on the existence of quantized energy levels in atomic systems while others explore different aspects of the concept. The discussion does not reach a consensus on the broader implications or interpretations of energy quantization.

Contextual Notes

Some claims rely on specific definitions of quantization and may depend on the context of bound states in quantum mechanics. The discussion includes references to mathematical derivations and experimental observations, but these are not universally accepted as definitive conclusions.

Mitadru Banik
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Why this quantization of energy term occur in quantum mech?

Why this "quantization of energy" term occur in quantum mech? Is there any real physical example of quantization of energy? or its just a thought? As i know that if a particle is bound in between two potential walls then the energy of the particle is quantized i.e. E<V(x).
 
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Energy of electron in atomic orbital is quantized. That is a real physical example.

For more details you can check past discussions on this topic. You can find them at the bottom of this page under "Similar discussions for: Quantization of energy".
 
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A convenient way to think about 'quantization' of energy is via Planck's constant, h.
see for example:
http://en.wikipedia.org/wiki/Quantum_Of_Action

[look for 'h' in the early formulas...]

... [Max] Planck discovered that physical action ... must be some multiple of a very small quantity (later to be named the "quantum of action" and now called Planck's constant). This inherent granularity is counterintuitive in the everyday world, where it is possible to "make things a little bit hotter" or "move things a little bit faster". This is because the quanta of action are very, very small in comparison to everyday macroscopic human experience...

So quantum actions are discrete, take place in small 'bumps', are not continuous. Another example is the kinetic energy of photoelectric electrons:

http://en.wikipedia.org/wiki/Photoelectric_effect#Mathematical_description

note the 'h' within the formula...
 
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Mitadru Banik said:
Why this "quantization of energy" term occur in quantum mech? Is there any real physical example of quantization of energy? or its just a thought? As i know that if a particle is bound in between two potential walls then the energy of the particle is quantized i.e. E<V(x).
This is observed experimentally in atomic spectra which show discrete spectral lines associated with discrete energy differences.ä

And it is derived mathematically via the Schrödinger equation having discrete eigenvalues for bound states. So the discrete energy levels in atomic spectra can be calculated (in most cases numerically)
 
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