Quantization of Energy in Quantum Mechanics - Real Examples?

In summary: Schrödinger equation.In summary, the quantization of energy in quantum mechanics refers to the observation and mathematical derivation of discrete energy levels, rather than a continuous spectrum, in certain systems such as atomic spectra and bound particles. This is due to the inherent granularity of physical action, as described by Planck's constant.
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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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FAQ: Quantization of Energy in Quantum Mechanics - Real Examples?

What is quantization of energy in quantum mechanics?

Quantization of energy in quantum mechanics is the concept that energy can only exist in discrete, quantized levels rather than being continuous. This means that energy can only take on specific, fixed values rather than any value in between.

Why is quantization of energy important in quantum mechanics?

Quantization of energy is important in quantum mechanics because it explains many observed phenomena that classical mechanics cannot, such as the discrete energy levels of atoms and the stability of matter. It also plays a crucial role in understanding the behavior of particles at the subatomic level.

Can you provide real-life examples of quantization of energy?

Yes, one example is the energy levels of electrons in an atom. According to the Bohr model of the atom, electrons can only exist in specific energy levels, and when they transition between levels, they emit or absorb energy in discrete packets called photons. Another example is the energy levels of vibrations in a molecule, which determine the frequencies of infrared radiation that the molecule can absorb.

How does quantization of energy relate to the uncertainty principle?

The uncertainty principle states that it is impossible to know the exact position and momentum of a particle simultaneously. In quantum mechanics, energy and momentum are closely related, so the uncertainty principle also applies to energy. This means that the more precisely we know the energy of a particle, the less we know about its momentum, and vice versa.

Is quantization of energy a fundamental law of nature?

Yes, quantization of energy is a fundamental law of nature in the realm of quantum mechanics. It is supported by a vast amount of experimental evidence and is a core principle in understanding the behavior of particles at the subatomic level. It is also essential in many modern technologies, such as transistors and lasers, which rely on the quantization of energy in semiconductors.

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