How can I apply quantum mechanics to describe a photon gas in a box?

In summary, the conversation is about solving the particle in a box problem with a massless photon, specifically the "photon gas in a box" problem. The equations for electromagnetic radiation give quantized energy, similar to those for a particle in a box, but the approach using classical standing waves is also mentioned. The question is about how to treat these photons using quantum mechanics. Additional resources are provided for further information.
  • #1
Amok
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I should know how to do this, but I've been getting a bit confused. Can you solve the particle in a box problem considering that the particle is a massless photon? I'm not so sure on how to write the Hamiltonian correctly for this problem.

EDIT: Ok, to add some information, I'm actually looking at the "photon gas in a box" problem, and apparently the equations describing the electromagnetic radiation give quantized energy (just like the one for a particle in a box), but I can't seem to get there by myself. Maybe there's some fundamental thing I'm not getting.
 
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  • #2
Your question is reffering to the wave function of a photon or to the photon gas problem ?

You can take a look here for the first:
The photon wave function , I. Bialynicki-Birula , Coherence and Quantum Optics VII, Eds. J.H.Eberly, L.Mandel, and E.Wolf., Plenum, New York, 1996, p. 313

You can get the article from the author's web page.

The second is, if i remember correctly, a standard problem found in many books on Statistical Mechanics.

Additionally, take a look here
https://www.physicsforums.com/showthread.php?t=206721
 
  • #3
|squeezed> said:
Your question is reffering to the wave function of a photon or to the photon gas problem ?

You can take a look here for the first:
The photon wave function , I. Bialynicki-Birula , Coherence and Quantum Optics VII, Eds. J.H.Eberly, L.Mandel, and E.Wolf., Plenum, New York, 1996, p. 313

You can get the article from the author's web page.

The second is, if i remember correctly, a standard problem found in many books on Statistical Mechanics.

Additionally, take a look here
https://www.physicsforums.com/showthread.php?t=206721


Thank you for replying. I understand the statistical mechanics part of it well. In my course (which is about statistical mechanics), the electromagnetic radiation inside the box is treated classically, by using standing waves (which actually gives rise to quantization!). I don't really need to know this, I was wondering how you would treat those photons with QM. Once again, thanks for replying, I'll be sure to check out the info you gave me as soon as I have the time.
 

Related to How can I apply quantum mechanics to describe a photon gas in a box?

1. What is a photon in a box?

A photon in a box is a theoretical concept used in basic quantum mechanics to explain the behavior of a single photon confined in a closed container or "box". This box can be any shape or size, but it is typically visualized as a cube or rectangular prism. The photon in this scenario is treated as a particle, and its energy and momentum are quantized.

2. How does a photon behave in a box?

In this simplified model, a photon in a box can only exist in certain energy levels, known as "quantum states". These states are determined by the dimensions of the box and the properties of the photon, such as its wavelength. The photon can also exhibit wave-like properties, as it can "tunnel" through the walls of the box with a certain probability.

3. What is the significance of studying a photon in a box?

Studying a photon in a box allows scientists to understand the fundamental principles of quantum mechanics, such as quantization of energy and particle-wave duality. It also provides insight into more complex systems, as the concept of a confined particle can be applied to atoms, molecules, and other particles.

4. How does the energy of a photon in a box relate to its wavelength?

The energy of a photon in a box is directly proportional to its wavelength. This relationship is known as the Planck-Einstein relation, which states that the energy of a photon is equal to Planck's constant (h) multiplied by the frequency of the photon (f). Since frequency and wavelength are inversely related, the energy of a photon in a box can also be expressed as h over the wavelength (λ).

5. Can a photon in a box have a zero energy state?

No, according to the principles of quantum mechanics, a photon in a box cannot have a zero energy state. This is because the uncertainty principle states that the position and momentum of a particle cannot both be precisely known. Therefore, a photon in a box must have a minimum energy level, known as the zero-point energy, even if it is at rest.

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