Probability Wave Explained

[MetaFrizzics]

Waves are waves. What is a probablity wave?

This seems like a fun question to answer:

 

You have a wave function (a function of time or position).

This represents in a 'one step removed' fashion the probability of a particle's position being someplace or in some state. You get the actual probability by squaring the instantaneous amplitude of the wave at a given time or place.

 

This (always positive) number which is less than or equal to 'one' represents the probability of the particle being found at a certain location and/or time. i.e., .5 means a 50% chance of the particle being found there.

 

 

Notice that the Wave Function isn't directly describing the photons travelling through space: Instead the wave equation (properly set up and with the portion of interest isolated) describes the probability of a photon hitting a given surface, defined some fixed distance away from the two slits. So if enough photons hit the surface, a spotted pattern develops which approximates the probability wave (wave function squared) for that surface:

 

[eon_rider]

Great picture of the two slit experiment!

 

I remember doing it in college (uni) but it never looked that colorful.

 

Also...where is the original question posted? (scratches head)

"Waves are waves. What is a probablity wave?"

As yours is the first post in this thread.

 

No biggie, just curious.

 

Cheers for the graphics and the info.

 

Eon.

[DQW]

This (always positive) number which is less than or equal to 'one' represents the probability of the particle being found at a certain location and/or time.

No doubt, you mean it "represents the probability of being found within a certain interval of space at a certain time".

 

The probability of being found at a certain location is always zero (unless you can show me a system that has discrete position eigenvalues).

[MetaFrizzics]

Thanks for the corrections of detail.

I thought these pictures would be helpful for those just starting out.

I modified some original pics found on the web (quite significantly) for clarity,

and added pics and text of my own. Textbooks are usually so dry that the reader is left with no picture at all (figuratively as well!).