# complex

1. ### varying vev for a scalar field of complex charge, such as as the Higgs field

Here is some background for my question, which is as I currently understand it (meaning, it may be wrong): In a self-interacting scalar field, the formula for potential energy can be given as (μ^2 * (Φ^2)/2) + (λ * (Φ^4)/4). In a field with an imaginary value for μ, μ^2 becomes negative...
2. ### complex algerbra

prove by contour integration that ∮▒sin⁡〖mx dx〗/x =π/2
3. ### On the nonsense of complex springs

I've just been attending lectures on differential equations at the university of YouTube :) Noticed something interesting... For a simple spring system F= -kx so mx'' = -kx or x''+kx/m = 0. This is a homogeneous 2nd order linear DE so the solutions are: x = e^{+/- i*sqrt(k/m)} where i...
4. ### Is complex valued psi really ontological?

I have been playing around with fourier transforms on Wolfram Alpha. I noticed that F{cos kt, w} = sqrt(pi/2)*diracDelta(k+/-w) where +/- means either + or - and w is the frequency transform variable. I discovered to my amazement that the fourier transform F{cos(kt+phi),w} =...
5. ### Are wave functions really complex?

Why is the wave function complex containing both a real and imaginary part? The wave function I am talking about is the one which when you take the square of it it gives the probability density distribution of where the particle might be found. Are we saying that the real world has an...
6. ### Complex car chase

Okay heres the deal: Cop passes a car that is speeding going 86 miles per hour. The cop slows down in order to turn around but must allow cars that are behind him to pass, so before he is able to turn around and begin pursuit, 33 seconds pass. The cop drives down the road A for about 1.6 miles...
7. ### Refractive idex of a liquid in a complex situation

An equiconvex lens, of refractive index 1.5, is in contact with a liquid layer on top of a plane mirror. A small needle with its tip on the principal axis is moved along the axis until its inverted image is found at the position of the needle. The distance of the needle image from the lens is...