What is the relation between wave function on a photon

In summary, the conversation discusses the wave equation and its relation to the double slit experiment. It explains how the wave equation can be used to calculate the probability of a photon hitting a certain point on the screen, and how this relates to the concept of wave function in quantum mechanics. The conversation also mentions alternative approaches to analyzing the experiment, such as using the Helmholtz equation.
  • #1
Tigersharkmks
4
0
... and its classical wave equation?
Suppose in our double sit experimental setup with the usual notion of d,D we have a light of known frequency (v) and wavelength (L)- so its y=Asin(kx-wt). It passes through the two hole and move ahead doing the usual interference stuff, so final wave equation will be y =y1 + y2 = 2A*cos(u/2)*sin(kx-wt+u/2) where u is the phase difference. We can convert phase difference 'u' to path difference 'q'. Now we choose the point of interest on screen (s) which essentially depend upon q. So the final y at s is y=2A*cos(a*s)sin(kx-wt+a*s) where a is constant. Now this y implies a set of wave (because different values s corresponds to interference of different wave with different phase difference) and is function of variable s,x,t. Now since I have put screen at some x (=D), therefore the y reduces to function of two variable s,t. Now rewriting y=2A*cos(u/2)sin(u/2 -wt +kD) which is also a wave equation (but with different meaning). Now the screen acts as our x-axis (or to be precise u-axis). Now intensity is proportional to to sq of wave eqn written above which in turns depends upon u. And what we know is intensity is proportional to number of photon, so we postulate that probability of a photon to hit certain u is proportional to intensity = wave eq ^2. Now is the function y I have written above is psi(wave function) of quantum mechanics with u acting as x(in psi). If not, then what is their relation between them. I have other things to ask depending upon your response. Thank you!
 
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  • #2
Forget this wave particle analysis of the double slit:
http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

What's really going on is this.

Consider just one slit for a moment and we will use electrons for definiteness. Just behind the slit it has a definite position along the screen. This means its momentum along the screen is totally unknown so it will scatter in an unknown direction and hit the screen at an unknown location. Now imagine you have two slits - its not in a definite position behing the screen because a detector placed just behing the screen will give either one or the other slit. This means its state is a superposition of the states of exact position - and that why you get interference.

If you insist on that kind of analysis see the following:
http://arxiv.org/abs/1009.2408

But its a more difficult approach showing the Schroedinger's equation reduces to the Helmholtz Equation.

Thanks
Bill
 

1. What is a wave function?

A wave function is a mathematical representation of the quantum state of a particle, such as a photon. It describes the probability of finding the particle in a certain state at a given time.

2. How does a wave function relate to a photon?

A photon, being a fundamental particle of light, also has a wave-like nature, meaning it can be described by a wave function. The wave function of a photon represents the probability of finding the photon at a specific location in space.

3. What is the significance of the wave function on a photon?

The wave function of a photon is significant because it provides a way to understand and predict the behavior of light at the quantum level. It allows scientists to make calculations and predictions about the behavior of photons in various situations.

4. How is the wave function of a photon measured?

The wave function of a photon is not directly measurable, but its effects can be observed through experiments, such as the double-slit experiment. The wave function can also be indirectly measured through techniques such as quantum tomography.

5. Can the wave function on a photon be manipulated?

Yes, the wave function of a photon can be manipulated through various processes, such as interference, polarization, and entanglement. These manipulations can change the behavior and properties of the photon, allowing for applications in technologies such as quantum computing and communication.

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