Introduction to quantum mechanics

[Mppl]

I'm having a course about introduction to quantum mechanics and I am having a lot of problems understanding the derivation of the Rayleigh-Jeans Law which was an attempt to explain the black body radiantion expectrum with classical arguments.
My main problem is:
they assumed that matter was made of vibrating charges, and because they were vibrating they produced electromagnetical radiation till now no problems.
they they said, well if we know the mean value of the energy of each of these particles and we know the number of charges that vibrate with f between f and f+df we know the energy emited between those frequencies, well I can leave with that, but then they make the assumption that somehow the number of charges that vibrate between those 2 frequencies (and assuming that the black body is cubic a box with a small hole in it) is given by the number of stacionary waves that have frequencies between the 2 values I mentionated devided by the box volume...how can it be? I am certainly missing a step here...can someone explaining it to me?

 

[eljose79]

Hello there,

I can understand your confusion with the derivation of the Rayleigh-Jeans Law. It is indeed a complex concept and requires a good understanding of quantum mechanics and classical arguments.

Firstly, the Rayleigh-Jeans Law was an attempt to explain the black body radiation spectrum using classical arguments. This means that the scientists at that time were trying to use classical physics principles to explain a phenomenon that was later found to be governed by quantum mechanics.

Now, in order to explain the black body radiation spectrum, the scientists assumed that matter was made of vibrating charges. This is a classical argument as it is based on the classical understanding of matter. They believed that these vibrating charges would produce electromagnetic radiation.

Next, they made the assumption that the mean value of the energy of each of these vibrating charges would determine the energy emitted at a particular frequency. This also makes sense as the more energy a vibrating charge has, the more electromagnetic radiation it would emit.

Now, here comes the tricky part. They then assumed that the number of charges vibrating at a particular frequency within a given range (say, between f and f+df) would be directly proportional to the number of stationary waves that exist within that frequency range. This means that if there are more stationary waves of a particular frequency within a given volume (in this case, the cubic box with a small hole in it), then there would be more vibrating charges at that frequency within that volume.

This assumption was based on the classical understanding of waves and their behavior, which was later found to be incorrect when quantum mechanics was introduced. In quantum mechanics, particles can exist as both waves and particles, and their behavior is described by wave functions. Therefore, the assumption that the number of vibrating charges is directly proportional to the number of stationary waves is not entirely accurate.

I hope this explanation helps you understand the derivation of the Rayleigh-Jeans Law better. I would suggest delving deeper into the concepts of quantum mechanics to fully understand this phenomenon. Keep exploring and don't hesitate to ask for clarifications. Best of luck with your studies!