Can we derive quantification of energy mathematically?

In summary: I'm going to check it out!In summary, the author is discussing the quantization of energy in terms of resonance and how it relates to classical mechanics and electrical systems. Resonances are quantized when energy is transferred, but this does not mean that the amount of energy is quantized.
  • #1
svletana
21
1
I'm studying for my introduction to modern physics exam, and reading about the ultraviolet catastrophe and why equipartition theorem stops working to explain blackbody emissions for high frequencies I was thinking if we could use the theorem to arrive at the quantification of energy (probably the answer is no).

I remember my professor saying that at some point we'll learn how we can arrive at the quantification of energy from some hypotheses, but I don't remember what that was.

Thanks!
 
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  • #2
Quantization of energy appears when you solve Schrodinger's equation in many problems We can only guess at what your professor was thinking, but there's a fair chance that that's what it was.
 
  • #3
Is it correct to say resonance in a classical mechanical or electrical system is quantisation of energy?
 
  • #4
Nugatory said:
Quantization of energy appears when you solve Schrodinger's equation in many problems We can only guess at what your professor was thinking, but there's a fair chance that that's what it was.
You're right, Thank you!
 
  • #5
houlahound said:
Is it correct to say resonance in a classical mechanical or electrical system is quantisation of energy?
No. The system can have any value of energy. Resonances are related to the transfer of energy, not it's amount.
 
  • #6
Makes sense, I have always held the analogy when looking at atomic spectra as that of striking a bell with a hammer and looking at the non transient part of the ringing bell's frequency spectrum.

Can you help with the analogy if it is not OT.
 
  • #7
Its deep, beautiful and powerful:


Mostly it is quantisised but the why will take you on a VERY interesting journey.

Thanks
Bill
 
  • Like
Likes houlahound
  • #8
Unfortunately my phone overheats and shuts down after 20mins of YouTube so yet to watch the second half. That lecturer is a clever, passionate and gentle teacher. Gonna follow his clips.

Thanks for a great link.
 

FAQ: Can we derive quantification of energy mathematically?

How can energy be quantified mathematically?

The quantification of energy can be achieved by using mathematical equations that relate energy to other physical quantities, such as mass, velocity, and distance. These equations are based on fundamental principles of physics, such as the law of conservation of energy and the relationship between energy and work.

Why is it important to derive quantification of energy mathematically?

Deriving the quantification of energy mathematically allows for a deeper understanding of how energy works and how it can be measured. It also provides a universal and objective way to quantify energy, which is crucial for scientific research and technological advancements.

What are some examples of mathematical equations used to quantify energy?

Some common equations used to quantify energy include the kinetic energy equation (KE = 1/2mv^2), the potential energy equation (PE = mgh), and the work-energy theorem (W = Fd). These equations can be applied to different systems and scenarios to determine the amount of energy present.

Are there any limitations to deriving quantification of energy mathematically?

While mathematical equations are a powerful tool for quantifying energy, they do have some limitations. For instance, they may not accurately account for all factors that affect energy, such as friction or air resistance. Additionally, some systems may be too complex to be accurately quantified using mathematical equations alone.

How does the quantification of energy mathematically contribute to advancements in science and technology?

The ability to mathematically quantify energy has been crucial for advancements in various fields, such as engineering, physics, and chemistry. It has allowed for the development of new technologies, such as renewable energy sources and energy-efficient devices, and has also led to a better understanding of natural phenomena, such as climate change and the behavior of particles in the universe.

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