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### Topic: Uses of complex numbers  (Read 8841 times)

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#### itsmexD

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##### Uses of complex numbers
« on: January 09, 2012, 05:33:45 PM »
Hey guys,
For school I'm doing a sort of report (don't know a better word for it) on complex numbers and what they are used for. I've been going through books in the library and searching the internet hoping to find what they're used for in chemistry, but I can't find anything. So, I was hoping anyone here could help me out ='] I don't need very detailed descriptions, very briefly would be perfect.
Thank you!

#### Jorriss

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##### Re: Uses of complex numbers
« Reply #1 on: January 09, 2012, 09:32:34 PM »
Non-relativistic Quantum Mechanics - the schroedinger equation itself is a complex valued differential equation.

Just about any time one has a trigonometric function it is easier to handle in terms of complex exponentials. You may also wish to look up steepest descent (asymptotic expansions), evaluating integrals by residue methods and branch cuts.

I can give you more if you would like though.

#### MrTeo

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##### Re: Uses of complex numbers
« Reply #2 on: January 10, 2012, 03:05:29 AM »
I've been going through books in the library and searching the internet hoping to find what they're used for in chemistry, but I can't find anything.

Er...

http://en.wikipedia.org/wiki/Complex_number#Applications
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#### itsmexD

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##### Re: Uses of complex numbers
« Reply #3 on: January 10, 2012, 01:28:15 PM »
Those are all uses of complex numbers mainly focussed on physics and mathematics (though, not sure whether I'd call quantum mechanics more physical than chemical), and that wasn't really the point, but thanks anyway =] Same goes for the wikipedia article. My problem is finding uses for complex numbers specifically in chemistry.

#### juanrga

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##### Re: Uses of complex numbers
« Reply #4 on: January 10, 2012, 02:30:20 PM »
Those are all uses of complex numbers mainly focussed on physics and mathematics (though, not sure whether I'd call quantum mechanics more physical than chemical), and that wasn't really the point, but thanks anyway =] Same goes for the wikipedia article. My problem is finding uses for complex numbers specifically in chemistry.

Complex numbers are used all the time in quantum chemistry, spectroscopy (a branch of physical chemistry) in the ways said to you before by other posters.

In nuclear chemistry, often the evolution of instable nuclei (exponential decay) is modeled by adding an imaginary term iGamma to the nuclei quantum Hamiltonian H.

Complex numbers are also used in chemical reaction theory. A transition structure is characterized by the presence of imaginary frequencies, for instance.
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