Interference of Probability Waves: A Quantum Physics Intro

[nouveau_riche]

i am new to quantum physics,can anyone help me with this

can probability waves interfere?or they can produce an interference pattern?

 

[Naty1]

sure they do.

A particle is a limited space of energy where constructive inteference has occurred. A particle is a bundle, or quanta, of energy or momentum quantum fields which spread everywhere. And a particle such as an orbital electron can be thought of as a resonant cavity, a confined wave, a standing wave, having a discrete series of frequencies.

 

[nickthrop101]

yes that can, when a whole group of particles are placed in close proximaty to each other then their interference acts positively to create a larger posibilaty that you'll find that object there, aka, the probability spike gets larger in that position. That is why you do not see a cricket bat changing position suddenly, as the probabilty wave for that bat being there is so large that the chances that it will be somewhere else are nigh-on-impossible, but not impossible :)

 

[jtbell]

can probability waves interfere?or they can produce an interference pattern?

Yes. An experiment similar to two-slit interference for light, has been done with electrons:

http://www.hitachi.com/rd/research/em/doubleslit.html

Note carefully that the interference pattern appears (gradually) even when only one electron at a time passes through the apparatus.

 

[edguy99]

i am new to quantum physics,can anyone help me with this

can probability waves interfere?or they can produce an interference pattern?

They have a "probability" of interference that varies in a regular way both over time and space.

 

[nouveau_riche]

Yes. An experiment similar to two-slit interference for light, has been done with electrons:

http://www.hitachi.com/rd/research/em/doubleslit.html

Note carefully that the interference pattern appears (gradually) even when only one electron at a time passes through the apparatus.

They have a "probability" of interference that varies in a regular way both over time and space.

but probability waves are not similar to that of water waves,they just represent probabilities to localize a particle,if two particles just hit the same point in space,then it will be a particle collision not interference

 

[SpectraCat]

but probability waves are not similar to that of water waves,they just represent probabilities to localize a particle,if two particles just hit the same point in space,then it will be a particle collision not interference

Really? Are you sure? How would you go about proving that statement? What kinds of particles are you talking about? For example, do you think your statement is true for photons?

One important aspect of QM that you may be missing by talking about "probability waves" is phase. In general, probability distributions are obtained by taking the square modulus of the wavefunction, thereby destroying all information about the complex phase of the underlying wavefunction. Since it is phase relationships between wavefunctions that are responsible for determining interference, you can't really get interference between "probability waves", given that definition. However, according to the Born interpretation, the significance of the wavefunction is that it is a "probability amplitude", so if you are talking about the *wavefunction* when you say "probability wave", then yes, you can still get interference, but I would strongly suggest that you drop the terminology of "probability wave" and just say wavefunction instead.

 

[nouveau_riche]

Really? Are you sure? How would you go about proving that statement? What kinds of particles are you talking about? For example, do you think your statement is true for photons?

One important aspect of QM that you may be missing by talking about "probability waves" is phase. In general, probability distributions are obtained by taking the square modulus of the wavefunction, thereby destroying all information about the complex phase of the underlying wavefunction. Since it is phase relationships between wavefunctions that are responsible for determining interference, you can't really get interference between "probability waves", given that definition. However, according to the Born interpretation, the significance of the wavefunction is that it is a "probability amplitude", so if you are talking about the *wavefunction* when you say "probability wave", then yes, you can still get interference, but I would strongly suggest that you drop the terminology of "probability wave" and just say wavefunction instead.

how can you get interference pattern?,as i know it to my knowledge,the probability amplitude represent the probability of localizing a particle in a region in space,so if two particle hit the region of space at the same moment,there will be a collision,not interference

 

[SpectraCat]

how can you get interference pattern?,as i know it to my knowledge,the probability amplitude represent the probability of localizing a particle in a region in space,so if two particle hit the region of space at the same moment,there will be a collision,not interference

I know you think that, but it is not correct. For example, how can mass-less particles like photons undergo collisions? Even for massive particles, you have BEC states that allow an arbitrary number of spin-zero bosons to populate the same quantum state. That is not quite the same thing as having particles localized to the same point in space, but the differences are subtle ... for such BEC's, adding more particles simply increases the amplitude of the wavefunction at all points in space simultaneously.

Regarding the other part of your statement ... it is a result of the complementarity of quantum states. If you try to measure interference, then you observe the wave nature of the quantum states. If you try to localize the particle onto a detector, then you observe the particle-like nature of the states. It is worth noting that observing the wave-nature of quantum states seems to require more indirect measurement techniques, which often involve particle-like measurements on large ensembles of identically prepared particles. It is hard to think of an experiment where the wave-like nature of a single quantum state is observed directly, meaning it is clear for each individual particle, and not just for an ensemble.