Many-Particle Wavefunction Question

[CuriousLearner8]

TL;DR Summary

Multi-particle wavefunction testable results?

Hello,

I hope you are well.

I have been doing a lot of readings on the wavefunction and have a question I did not see asked anywhere else in these forums. I was wondering if someone could shed some light on this for me?

I know the wavefunction is in 3N coordinate space and could be used to describe multiple particles. The greatest triumphs of Quantum Mechanics comes from single particle wavefunctions, however, such as predicted the spectra of hydrogen-like atoms. What are some examples of multiple-particle wavefunctions producing testable predictions that have been measured in the laboratory? If you have some papers I could read or look up, that would be most appreciated.

Thank you to you all.

 

[vanhees71]

Any multi-electron atom (i.e., any atom other than hydrogen) is an example for the success of many-particle physics, and it can be described by non-relativistic 1st-quantized multi-electron wave functions.

 

[CuriousLearner8]

Any multi-electron atom (i.e., any atom other than hydrogen) is an example for the success of many-particle physics, and it can be described by non-relativistic 1st-quantized multi-electron wave functions.

My understanding that no multi-electron atom has been successfully described by a multi-electron wavefunction because the math becomes difficult to disentangle. Did I misunderstand?

 

[PeroK]

My understanding that no multi-electron atom has been successfully described by a multi-electron wavefunction because the math becomes difficult to disentangle. Did I misunderstand?

Yes, you misunderstood. Few problems in physics lead to closed form solutions. Even the three-body classical gravitational problem does not have a general closed form solution.

https://en.wikipedia.org/wiki/Closed-form_expression

https://en.wikipedia.org/wiki/Three-body_problem

This means that the solutions to specific physics problems lead to numerical approximations, that are nevertheless equally valid solutions to the problem.

 

[CuriousLearner8]

Yes, you misunderstood. Few problems in physics lead to closed form solutions. Even the three-body classical gravitational problem does not have a general closed form solution.

https://en.wikipedia.org/wiki/Closed-form_expression

https://en.wikipedia.org/wiki/Three-body_problem

This means that the solutions to specific physics problems lead to numerical approximations, that are nevertheless equally valid solutions to the problem.

Thanks for the response. I'm genuinely curious. What numerical approximations have we used for multi-particle systems? I'd like to learn more.

 

[CuriousLearner8]

Thanks for the response. I'm genuinely curious. What numerical approximations have we used for multi-particle systems? I'd like to learn more.

I'm very interested in close approximations matching experimental results. I'm working on a project, hence these questions.

 

[PeroK]

Thanks for the response. I'm genuinely curious. What numerical approximations have we used for multi-particle systems? I'd like to learn more.

After hydrogen comes helium:

https://www.math.hmc.edu/~dyong/math164/2007/reed/finalreport.pdf

One of the main hopes of quantum computing is that it will provide further numerical solutions to problems that are too hard for classical methods. E.g. optimising the production of ammonia:

https://digitalcommons.dartmouth.edu/cgi/viewcontent.cgi?article=1031&context=dujs

 

[CuriousLearner8]

After hydrogen comes helium:

https://www.math.hmc.edu/~dyong/math164/2007/reed/finalreport.pdf

One of the main hopes of quantum computing is that it will provide further numerical solutions to problems that are too hard for classical methods. E.g. optimising the production of ammonia:

https://digitalcommons.dartmouth.edu/cgi/viewcontent.cgi?article=1031&context=dujs

Many thanks for these. If anyone has other examples as well, they would be much appreciated.

 

[PeroK]

Many thanks for these. If anyone has other examples as well, they would be much appreciated.

Mr Google might have a few!

 

[CuriousLearner8]

Mr Google might have a few!

I have checked, but seeking further input. :-)

 

[Haborix]

This link may give you some ideas. Searching quantum chemistry is probably going to get you better results than multi-particle wavefunction.

 

[hutchphd]

Much of solid state physics involves multiparticle solutions. Because of the periodicity it is often possible to find collective motions that look like nearly free quantum particles.
There are folks who have spent careers calculating the electron density in real world atoms to the precision afforded by the latest supercomputer.
And as @Haborix points out computational quantum chemistry is a real thing.

 

[fluidistic]

A.bit surprised nobody explicitely mentioned ''density functional theory'', or ''DFT''. Those are terms the OP should google and wikipediade.

 

[CuriousLearner8]

Much of solid state physics involves multiparticle solutions. Because of the periodicity it is often possible to find collective motions that look like nearly free quantum particles.
There are folks who have spent careers calculating the electron density in real world atoms to the precision afforded by the latest supercomputer.
And as @Haborix points out computational quantum chemistry is a real thing.

This is very fascinating.