Math exploration - Gauss. Any idea?

[VicGarcia]

Hi all! I am cursing my 2nd year on the IB Programme and this is the start of my hell... I'm on HL Maths (why god?) and i have to do my math exploration.

I would like to do it about Gaussian distributions (i love stadistic), but i have no idea how to start... I need to take something with applications in real life, but i don't know what can I do...

Has anyone any idea of what can I do? Thanks all

 

PD. Sorry about my english, i'm good speaking it but writing...

[Baller97]

I have no idea either.. I'll be watching this post

[VicGarcia]

Help please, i need to know what to do for this thursday :/

[JamalS]

Gaussian distributions appear in many areas of physics. You could choose to explore the quantum harmonic oscillator, and solve the time-independent Schrodinger equation, demonstrating the ground state wavefunction is in fact a Gaussian, by directly solving the differential equation, or using Dirac's ladder operator method. Another possibility: in quantum field theory, the partition function for a free scalar Klein-Gordon field requires the evaluation of a functional Gaussian integral - the investigation could be based on that.

 

If you enjoy the topic of integration and Gaussians, you could choose to base your exploration of methods of evaluating various Gaussian integrals; not just one-dimensional integrals, but perhaps of arbitrary dimension? There are many methods of approximation you could also explore, such as Laplace's method, or the method of steepest descent.

 

Gaussians appear in statistical treatments of problems in statistical physics and kinetic theory. (See the lecture notes by Professor D. Tong online.)