simulating quantum behavior
Author
Is there a good comprehensive resource for quantum mechanical rules?
I'd like something that I could translate to code.
I'd like to simulate a Hydrogen atom. I'm aware that even this would be extremely difficult.
I'd like this to obey all quantum mechanical phenomena. For example, without hard coding this type of behavior, I'd like to shove a planck's mass or more into the space of a planck's length or less and see it collapse into a singularity. (with singularities being some abstract concept, since they'd probably 1/0 the whole simulation if i tried to do them completely procedurally.) it's just the process of the singularity being formed that i'd like to be procedural. and this is just a random example i picked out of the air to describe what i meant by simulating a hydrogen atom on the quantum level. other phenomena would have to be present as well. all procedural except for things like singularities/strings etc.
You can find a lot of foundational information about quantum mechanics at wikipedia. Heisenberg's uncertainty principle will stymie your efforts. Schrodinger's equations can be plotted, but it describes the square of the wave function as a probability. Planck's length is 10^-33 cm. Imo, it's a limit on the granularity of space, in the same sense that the speed of light is a limit on velocity. At any rate, these difficulties shouldn't stop you from modeling an atom. You can take the easy route and depict electrons as tiny planets in orbit about the nucleus using known orbital patterns (s,p,d,f) or you can try to emulate them as clouds of probability.
Are you familiar with improper integrals in R3?
Here is the atomic orbital wave function for hydrogen.
W(x,y,z) = (c^(3/2)/sqrt(pi)) * e^(-c*sqrt(x^2+y^2+z^2))
where (x,y,z) = (x(t),y(t),z(t)), c > 0, c is constant, c = z/a0 where z is the nuclear charge and a0 is the Bohr radius.
The math gets worse from there.
Are you familiar with improper integrals in R3?
Here is the atomic orbital wave function for hydrogen.
W(x,y,z) = (c^(3/2)/sqrt(pi)) * e^(-c*sqrt(x^2+y^2+z^2))
where (x,y,z) = (x(t),y(t),z(t)), c > 0, c is constant, c = z/a0 where z is the nuclear charge and a0 is the Bohr radius.
The math gets worse from there.
I think what you need is the wavefunction equation LessBread gave you:
http://en.wikipedia.org/wiki/Hydrogen_atom
With that you can calculate the probability of finding an electron at position within r,theta and gamma by integrating the modulus of the wavefunction square.
http://en.wikipedia.org/wiki/Wave_function
But back to your simulation, if you have planck's constant-> 0, what it mean is that the energy is no longer quantised and I think you just fall back to classical mechanic.
http://en.wikipedia.org/wiki/Hydrogen_atom
With that you can calculate the probability of finding an electron at position within r,theta and gamma by integrating the modulus of the wavefunction square.
http://en.wikipedia.org/wiki/Wave_function
But back to your simulation, if you have planck's constant-> 0, what it mean is that the energy is no longer quantised and I think you just fall back to classical mechanic.
Quantum mechanics (Schrödinger/Dirac equation) can tell you how the wave function of a fix number of particles evolve but it does not model things like particle creation and annihilation. so you would never see the He atom emitting light, particle-antiparticle annihilation or effects like vacuum polarization. If you are interested in simulating such effects you need to make use of quantum field theory.
Peskin and Schroeder might be a good book to start if you already have a deep understanding of QM (and maybe classical field theory).
Also I don't know what you expect to see during a simulation, people often ask for a cross section and use QFT to calculate it. The reality does not look like what you learn in QM. For example the electron and proton in He atom are actually surrounded by a cloud of photons and interact by exchanging photons. The proton itself has a complex structure (There are much particles involved than just the uud quarks) and at last there is the vacuum which is also pretty complex.
Peskin and Schroeder might be a good book to start if you already have a deep understanding of QM (and maybe classical field theory).
Also I don't know what you expect to see during a simulation, people often ask for a cross section and use QFT to calculate it. The reality does not look like what you learn in QM. For example the electron and proton in He atom are actually surrounded by a cloud of photons and interact by exchanging photons. The proton itself has a complex structure (There are much particles involved than just the uud quarks) and at last there is the vacuum which is also pretty complex.
The wiki www.quantiki.org might be of interest for you. They also have a list of quantum computer simulators.
edit: Oh, nice accident. Have a look at Dobb's code talk's yesterday's item: Quantum Computing - Standing on the Shoulders of Giants :)
edit: Oh, nice accident. Have a look at Dobb's code talk's yesterday's item: Quantum Computing - Standing on the Shoulders of Giants :)
Author
i already knew all this.
was hoping someone had found a grand unified theory and was just waiting for an opportunity to show it off in a thread.
cuz that's basically what i need.
i'm currently simulating a human brain in real time down to the electron on my iphone. it's an app you can d/l for 99 cents.
but it uses a crappy statistical model for the electron positions.
electrons are point particles. they have NO size whatsoever.
was hoping someone had found a grand unified theory and was just waiting for an opportunity to show it off in a thread.
cuz that's basically what i need.
i'm currently simulating a human brain in real time down to the electron on my iphone. it's an app you can d/l for 99 cents.
but it uses a crappy statistical model for the electron positions.
electrons are point particles. they have NO size whatsoever.
Quote:Original post by AlphaCoder
i already knew all this.
Tja, good for you. Great way to appreciate.
Author
Quote:Original post by phresnelQuote:Original post by AlphaCoder
i already knew all this.
Tja, good for you. Great way to appreciate.
I do appreciate help. I was only pointing out what I knew so they could help me out with the stuff I didn't.
Sorry if that tears at your soul and devours your heart messily. Ambien will help you sleep.
Check out the Feynman lecture about quantum mechaincs (it's really good):
http://research.microsoft.com/apps/tools/tuva/
The quantum one is video 6. You have to watch it on the microsift site with the silverlight software, unfortunately. I tried finding the video on other sites but they all keep getting taken down.
http://research.microsoft.com/apps/tools/tuva/
The quantum one is video 6. You have to watch it on the microsift site with the silverlight software, unfortunately. I tried finding the video on other sites but they all keep getting taken down.
Author
yep microsoft went on a feynman vendetta recently. or i guess to be more precise a vendeta against feynman fans
but it's cool that the lectures are accessible.
i actually helped him write a few of his lectures.
but it's cool that the lectures are accessible.
i actually helped him write a few of his lectures.
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