The complex-numbers tag has no wiki summary.
16
votes
9answers
4k views
About the complex nature of the wave function?
1.
Why is the wave function complex? I've collected some layman explanations but they are incomplete and unsatisfactory. However in the book by Merzbacher in the initial few pages he provides an ...
7
votes
9answers
1k views
QM without complex numbers
I am trying to understand how complex numbers made their way into QM. Can we have a theory of the same physics without complex numbers? If so, is the theory using complex numbers easier?
7
votes
3answers
529 views
Physics math without $\sqrt{-1}$
The use of imaginary and complex values comes up in many physics/engineering derivations.
My question is
Is it making the process of derivation easier or is it essential without which it would be ...
6
votes
2answers
149 views
Is the step of analytic continuation unavoidable or can you model around it?
One sometimes considers the analytic continuation of certain quantities in physics and take them seriously. More so than the direct or actual values actually. For example if you use the procedure for ...
6
votes
2answers
534 views
complex numbers in optics
I have recently studied optics. But I feel having missed something important: how can amplitudes of light waves be complex numbers?
I suppose this is quite fundamental, but I do not find the answer ...
6
votes
2answers
233 views
Complex coordinates in CFT
The Setup: Let's say we want to study a Euclidean $\mathrm{CFT}_2$ on $\mathbb R^2$ with coordinates $\sigma^1$ and $\sigma^2$ and metric
$ds^2 = (d\sigma^1)^2+(d\sigma^2)^2$.
It seems to me that ...
4
votes
2answers
322 views
Amplitude of Probability amplitude. Which one is it?
QM begins with a Born's rule which states that probability $P$ is equal to a modulus square of probability amplitude $\psi$:
$$P = \left|\psi\right|^2.$$
If I write down a wave function like this ...
3
votes
0answers
108 views
Is there a physical motivation to study finite fields?
Clearly finite groups are of immense value in physics and these are also substructures of fields. However I never came across any computations involving finite fields at university and so I never ...
2
votes
2answers
139 views
In classical mechanics, are complex numbers unphysical? [duplicate]
Possible Duplicate:
Physics math without $\sqrt{-1}$
When I produce a complex final solution to a problem that began without complex coefficients at all, I have so far (with my limited ...
2
votes
1answer
136 views
Newton's law of gravitation in complex form
In an ebook about elementary complex analysis I came across Newton's law of universal gravitation with a complex valued function in place of $r(t)$. Can somebody please explain the intuition about how ...
2
votes
3answers
274 views
What is the rationale behind representing a state function by a complex valued function in QM?
What is the rationale behind representing a state function of an electron with a complex valued function $\Psi$. If only the probabilistic argument was required then why not represent it with just a ...
2
votes
3answers
303 views
Confused over complex representation of the wave
My quantum mechanics textbook says that the following is a representation of a wave traveling in the +$x$ direction:$$\Psi(x,t)=Ae^{i\left(kx-\omega t\right)}\tag1$$
I'm having trouble visualizing ...
2
votes
1answer
257 views
Deriving the Sommerfeld expansion by contour integration (Le Bellac p. 277)
In Le Bellac's statistical physics book he derives the Sommerfeld expansion by a contour integral.
The idea is to expand integrals of the type $I(\beta)\equiv \int_{0}^{\infty}d\epsilon\, ...
2
votes
1answer
145 views
Why can you re-write the functional measure of a real-valued field $\phi(x)$ as $\mathcal{D}\phi=\prod_{k_n^0>0}dRe \phi(k_n) d Im \phi(k_n)$?
This happens in Peskin and Schroeder, An Introduction to QFT, on page 285. They set out to calculate correlation functions for the free real-valued Klein-Gordon field $\phi(x)\in \mathbb{R}$. They ...
1
vote
1answer
144 views
Complex Potentials, Potentials and Fields
Suppose an electric field $E=-\nabla \psi$ where $\psi=-Q\ln r$ where $Q$ is just some constant and I have found its harmonic conjugate to be $-Q\theta+c$ where $c$ is some constant. What does it say ...
1
vote
0answers
22 views
What is the relationship between complex time singularities and UV fixed points?
In this paper it is described how the turbulent kinetic energy spectrum and the flatness (a measure for intermittency) are governed by the position of the (dominant) singularities of the solutions of ...
1
vote
0answers
174 views
Probability and probability amplitude
What made scientists believe that we should calculate probability $P$ as the $P = \left|\psi\right|^2$ in quantum mechanics? Was it the double slit experiment? How? Is there anywhere in the ...
0
votes
1answer
33 views
Work done by complex field on complex plane
A force field is given by $F = 3z+5$. Find the work done in moving an object in this force field along the parabola $z = t^2 + it$ from $z = 0$ to $z = 4+2i$.
I don't understand why conjugate ...
0
votes
1answer
385 views
Solving the time independent Schrodinger equation: Does a complex solution make sense?
In my notes, I have the Time Independent Schrodinger equation for a free particle
$$\frac{\partial^2 \psi}{\partial x^2}+\frac{p^2}{\hbar^2}\psi=0\tag1$$
The solution to this is given, in my notes, ...
0
votes
1answer
85 views
Two similar questions related to analytic continuation of a complex variable and its conjugate
See the scan attached below. Brown, in his QFT book, argues a certain way to do an integral. I understand that 1.8.13 or equivalently 1.8.14 can be performed once analytic continuation is done. I ...
0
votes
1answer
27 views
Phasor representation of voltage in frequency domain
In a text on application of electromagnetism in transmission line, there introduces a phasor for the voltage (in frequency domain)
$$\tilde{V}(x) = V^+e^{-i\beta x} + V^-e^{i\beta x.}$$
Here $V^+$ ...
0
votes
3answers
581 views
Absolute value sign when normalizing a wave function
I have solved the following problem from Griffiths "Introduction to Quantum Mechanics".
Consider the wavefunction:
$\Psi (x,t) = A e^{-\lambda |x|} e^{-i\omega t} $
Normalize $\Psi$.
Now, we ...
-1
votes
1answer
253 views
understanding of meaning of cauchy-riemann equations [closed]
take some complex valued function f(z) = f(x + iy) = u(x,y) +iv(x,y)
with u,v,x,y real valued variables/functions
there are relationships between the partial derivites of u and v that must hold in ...
