# Wave function of multiple particles

• Checkster2323
In summary: You may be able to calculate the average energy of the electrons in that volume, but you cannot calculate their individual energies. So, in a sense, the wavefunction for the system is "incomplete" too.
Checkster2323
I've got a question for you all.

if there is a wave-function for a single particle, such as a photon..

and there is a wave-function for an electron..

"A wave function in quantum mechanics describes the quantum state of an isolated system of one or more particles. There is one wave function containing all the information about the entire system, not a separate wave function for each particle in the system. Its interpretation is that of a probability amplitude. Quantities associated with measurements, such as the average momentum of a particle, can be derived from the wave function."

and electrons EMIT photons when dropping down in an fermi level, energy.. emitting radiation as the photon..

does the wave-function for the photon not exist WITHIN the wave-function of the electron ?
does it become part of the wave-function of the electron ?
it surely changes the wave-function of the electron.. either by momentum or angle ... but doesn't the wave-function of the photon somewhat exist within the electrons ?

Checkster2323 said:
does the wave-function for the photon not exist WITHIN the wave-function of the electron ?
does it become part of the wave-function of the electron ?
it surely changes the wave-function of the electron.. either by momentum or angle ... but doesn't the wave-function of the photon somewhat exist within the electrons ?

No, for all three questions. In quantum mechanics, a single wave function always describes the entire system, and in general there is no meaningful way of talking about the electron's and photon's wave functions as two things in their own right, let alone trying to think of one them as "contained" in the other. You have one system and one wave function that describes that system.

If the interaction between two things is weak enough, we may be justified in treating them as separate systems each with their own wave function. But when we do this, it's an approximation based on neglecting some or all of their interactions because they're weak enough to ignore - and that's not the case for a photon-electron emission interaction.

so how does it work in terms of the universal wave function ? my brain has its own wave-function (of the ensemble it is) and so does your brain..

and we exist within the universe.. so if there is indeed a universal wave-function.. do our brains wave-functions not exist within the wave-function for the universe ?

Checkster2323 said:
so how does it work in terms of the universal wave function ? my brain has its own wave-function (of the ensemble it is) and so does your brain..

and we exist within the universe.. so if there is indeed a universal wave-function.. do our brains wave-functions not exist within the wave-function for the universe ?

You've just put your finger on one of the reasons why after nearly a century we can still find serious philosophical problems behind quantum mechanics. Quantum mechanics is a theory about observations, and there's nowhere outside the universe where we can stand and make observations about the universe. David Mermin, when confronted with this question, once placed his tongue firmly in his cheek and answered "Shut up and calculate". (Quote also attributed to Feynmann, who didn't come up with it but probably would have if Mermin hadn't gotten to it first).

(If you search this forum for threads containing the word "interpretation" and "foundation", you will find... well, words fail me... you'll have to try it for yourself, and don't say you weren't warned).

Practically speaking, it doesn't matter. When we use Newton's laws to figure out planetary motion in the solar system, we can pretend that the sun and planets form an isolated system and ignore the perturbations introduced by the Andromeda galaxy's gravitational field, and when we're using quantum mechanics to figure out the interaction of an electron with the electromagnetic field/photons around it, we can ignore the contributions to the wave function from the walls of the laboratory and the trees growing outside.

Checkster2323 said:
so how does it work in terms of the universal wave function ? my brain has its own wave-function (of the ensemble it is) and so does your brain..

and we exist within the universe.. so if there is indeed a universal wave-function.. do our brains wave-functions not exist within the wave-function for the universe ?

But trying to formulate such a thing is not only not-trivial, it is also unimaginable. It all depends on how you define your "system".

Let's go back to something "simpler". Let's look at Avogradro's number of electrons in a certain volume. THAT is your entire system. This is definitely simpler than a system consisting of an entire universe. Now, can you write a completely wavefunction for that electronic system?

I will give you the answer: you cannot. You may be able to construct a Hamiltonian for it, but it is practically impossible to find the exact solution (wavefunction) to that Hamiltonian. This is the many-body problem, and this is why field of study such as condensed matter physics exists. We make approximations to varying degree of accuracy so that we can construct sufficiently-accurate wavefunctions that can describe such a system. We know this works in a certain range of boundary (example: Fermi liquid theory). But we also know the boundary where it doesn't work. It is not trivial.

So already, for something that appears to be simpler (a volume of electrons), we already have quite a limitation in describing the entire system. And now we want to consider the entire universe?

Zz.

Actually, the task of capturing a wave-function seems to now be down to a science.

As seen in this article D.A.R.P.A now has a method to capture the wave-function on high dimensional systems
http://www.rochester.edu/newscenter...que-efficiently-finds-quantum-wave-functions/
The result of every possible measurement on a quantum system is coded in its wave function, which until recently could be found only by taking many different measurements of a system and estimating a wave function that best fit all those measurements.

Just two years ago, with the advent of a technique called direct measurement, scientists discovered they could reliably determine a system’s wave function by “weakly” measuring one of its variables (e.g. position) and “strongly” measuring a complementary variable (momentum).

Researchers at the University of Rochester have now taken this method one step forward by combining direct measurement with an efficient computational technique.

The new method, called compressive direct measurement, allowed the team to reconstruct a quantum state at 90 percent fidelity (a measure of accuracy) using only a quarter of the measurements required by previous methods.

“We have, for the first time, combined weak measurement and compressive sensing to demonstrate a revolutionary, fast method for measuring a high-dimensional quantum state,” said Mohammad Mirhosseini, a graduate student in the Quantum Photonics research group at the University of Rochester and lead author of a paper appearing today in Physical Review Letters.

The research team, which also included graduate students Omar Magaña-Loaiza and Seyed Mohammad Hashemi Rafsanjani, and Professor Robert Boyd, initially tested their method on a 192-dimensional state.
Finding success with that large state, they then took on a massive, 19,200-dimensional state.
Their efficient technique sped up the process 350-fold and took just 20 percent of the total measurements required by traditional direct measurement to reconstruct the state.

The amplitude and phase of a Gaussian mode illuminating a custom phase mask (the initials of the University of Rochester). The data are reconstructed by the CDM method with N=19 200, and M/N=20% of the total measurements.

“To reproduce our result using a direct measurement alone would require more than one year of exposure time,” said Rafsanjani. “We did the experiment in less than 48 hours.”While recent compressive sensing techniques have been used to measure sets of complementary variables like position and momentum, Mirhosseini explains that their method allows them to measure the full wave function.Compression is widely used in the classical world of digital media, including recorded music, video, and pictures. The MP3s on your phone, for example, are audio files that have had bits of information squeezed out to make the file smaller at the cost of losing a small amount of audio quality along the way.In digital cameras, the more pixels you can gather from a scene, the higher the image quality and the larger the file will be. But it turns out that most of those pixels don’t convey essential information that needs to be captured from the scene. Most of them can be reconstructed later. Compressive sensing works by randomly sampling portions from all over the scene, and using those patterns to fill in the missing information.

Similarly for quantum states, it is not necessary to measure every single dimension of a multidimensional state. It takes only a handful of measurements to get a high-quality image of a quantum system.The method introduced by Mirhosseini et al. has important potential applications in the field of quantum information science. This research field strives to make use of fundamental quantum effects for diverse applications, including secure communication, teleportation of quantum states, and ideally to perform quantum computation. This latter process holds great promise as a method that can, in principle, lead to a drastic speed-up of certain types of computation. All of these applications require the use of complicated quantum states, and the new method described here offers an efficient means to characterize these states.

Research funding was provided by the Defense Advanced Research Projects Agency’s (DARPA) Information in a Photon (InPho) program, U.S. Defense Threat Reduction Agency (DTRA), National Science Foundation (NSF), El Consejo Nacional de Ciencia y Tecnología (CONACYT) and Canadian Excellence Research Chair (CERC).
I will assume, "behind the curtain", they are now at 100% as opposed to the publicly released 90%...
sounds silly I realize. But D.A.R.P.A appear to have so many new measurement tricks, that Heisenberg must be rolling over in his grave.

So my question now is this.. (no need for a new thread).. Once you capture the wave-function of a system (a brain).. do you have a duplicate of it ?

maybe by reconstructing it as a Hamiltonian in a matrice.. or, + ? . by using it as the "universal wave-function" of a baby universe for that ensemble ?
(ie reconstructing it in Monte-Carlo space/ k-space) but writing that space with the H

Checkster2323 said:
Actually, the task of capturing a wave-function seems to now be down to a science.

As seen in this article D.A.R.P.A now has a method to capture the wave-function on high dimensional systems
http://www.rochester.edu/newscenter...que-efficiently-finds-quantum-wave-functions/

I will assume, "behind the curtain", they are now at 100% as opposed to the publicly released 90%...
sounds silly I realize. But D.A.R.P.A appear to have so many new measurement tricks, that Heisenberg must be rolling over in his grave.

So my question now is this.. (no need for a new thread).. Once you capture the wave-function of a system (a brain).. do you have a duplicate of it ?

maybe by reconstructing it as a Hamiltonian in a matrice.. or, + ? . by using it as the "universal wave-function" of a baby universe for that ensemble ?
(ie reconstructing it in Monte-Carlo space/ k-space) but writing that space with the H

OK, a little bit of background info here.

1. If you do a search, there has been at least a couple of threads on this very topic. You might want to read those and get a more complete picture of what actually is being measured here, especially on the concept of "weak measurement". Or better yet, get the actual publication. (Hint: you cannot get the result with just ONE, or even few, measurements).

2. "DARPA" is a funding agency, very much like other funding agency in the US such as DOE, NSF, etc. They don't do anything. They simple give money, to put it crudely, to groups and institutions that proposed work that they deem to be worthwhile to fund. If you look closely, the group acknowledges SEVERAL other funding agencies. So it is a bit misleading to say that "... D.A.R.P.A now has a method to ... " or "... D.A.R.P.A appear to have so many new measurement tricks..." DARPA does not have any of these.

BTW, what does this have anything to do with the original topic of this thread?

Zz.

sorry, I was simply trying to determine whether or not one wave-function could be placed within" another one..

like a subset in a set.

I figured if you could successfully measure the entire wave-function of an ensemble, then you could reconstruct it and perhaps place others within the reconstructed space.
that's why I began with the photon in the electron metaphor

Checkster2323 said:
sorry, I was simply trying to determine whether or not one wave-function could be placed within" another one..

like a subset in a set.

Then your citation of the paper has no relevance, because that is not what that paper is about!

At this point, I have serious doubt that you even understand a simple derivation of a 'wavefunction' and its properties.

Zz.

Checkster2323 said:
does the wave-function for the photon not exist WITHIN the wave-function of the electron ?
does it become part of the wave-function of the electron ?
it surely changes the wave-function of the electron.. either by momentum or angle ... but doesn't the wave-function of the photon somewhat exist within the electrons ?
I think about this question sort of spectroscopically. A laser has atoms that all have the same energy transition level. So it sort of seems like that energy gap is part of the system, and part of each electron energy in the system. But if you were to look at an individual electron ... it might absorb yet another photon of another allowed energy transition, not emit the expected photon. Or it might never emit a photon.

An electron is just an electron. An electron in an atom has a set of allowed orbitals, and a nucleus nearby. Information about photons is within that set of allowed orbitals and nuclear proximity.

I'm not sure I quite get the question. I do see that the atom, that absorbs the energy from a former photon, has allowed energy transitions available to it. One would be back down, with a photon emission. So I sort of grant that there is "photon" information there, although it is just part of the information for a possible future photon.

If there were such a thing as a complicated wave-function for a brain, I don't think that is a mathematical duplicate to the original. But that is JMO. Even if the brain was 8 pounds of water, I don't really think there is any way to create an exact mathematical equivalent. I think the group that is using a novel measurement algorithm is still measuring very small systems ... and I have never understood quantum computing, so I have no idea of the cost-benefit of using a compression technique that might have loss of information.

the only reason I brought the paper into this was to show that we are now beginning to capture the wave-functions of ensembles, it seems people still fight this notion.

I believe we will eventually be able to capture the entire wave-function of systems. heck, I KNOW we will.

and I DO know the basics behind the wave-function, no I can't do math nor show equations, but I get the jist of it.

the wave-function is a summation, the amplification of waves as I understand it.. and the reason they can be added together, amplified, has a lot to do with the bosonic nature of the wave itself.. its constructive interference in a way.. the particle in question, the collapse.. is result of destructive interference.. and the reason the wave-function can be added together.. summed over histories, is because of that bosonic nature of the wave. waves can be in the same position in space and time... but matter cannot.. and matter is the result, effect of the destructive interference.. so the wave-function is the summation of everywhere that particle MIGHT be... in my no-university laymens way of seeing it...

I know.. its got momentum and angular aspects to it.. and quantum numbers must also be part of it.. but this is all of the top pf my head
correct me as you wish.I have a lot of questions in regards to wave-functions, but I was HOPING to do it in a forum with intelligent and willing minds.

as for why I began this thread.. I want to know if the entire wave-function of an ensemble CAN be known, NOW.

and if so.. if it might be possible, to get the wave-function of.. say.. a single piece of pulp from an orange...

then the whole section of an orange..
then an orange itself..

and if so.. would the wave-function of the pulp not be WITHIN the wave-function of the orange ?but the orange is only a metaphor.

I want to know if the wave-function for a BRAIN can be determined. NOW..

Checkster2323 said:
I know.. its got momentum and angular aspects to it.. and quantum numbers must also be part of it.. but this is all of the top pf my head
correct me as you wish.

I'm going to close this thread before someone takes you up on this suggestion and it gets ugly.

## 1. What is a wave function?

A wave function is a mathematical representation of the quantum state of a particle or system of particles. It describes the probability of finding a particle in a particular location or state at a given time.

## 2. Can a wave function describe multiple particles?

Yes, a wave function can describe the quantum state of multiple particles. The wave function of multiple particles is a complex-valued function that depends on the positions and other properties of all the particles in the system.

## 3. How is the wave function of multiple particles different from a single particle?

The wave function of multiple particles is a more complex mathematical function compared to that of a single particle. It takes into account the interactions and correlations between the particles, whereas the wave function of a single particle only describes the state of that individual particle.

## 4. What is the significance of the wave function of multiple particles in quantum mechanics?

The wave function of multiple particles is a fundamental concept in quantum mechanics. It allows us to predict the behavior and properties of a system of particles, such as the energy levels and probabilities of different outcomes, based on the quantum state of the system.

## 5. How is the wave function of multiple particles used in practical applications?

The wave function of multiple particles is used in various practical applications, such as in quantum computing and quantum cryptography. It also plays a crucial role in understanding and developing technologies like lasers and transistors.

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