Questions tagged [plane-wave]
132 questions
18
votes
3 answers
What is the physical significance of the imaginary part when plane waves are represented as $e^{i(kx-\omega t)}$?
I've read that plane wave equations can be represented in various forms, like sine or cosine curves, etc. What is the part of the imaginary unit $i$ when plane waves are represented in the form
$$f(x) = Ae^{i (kx - \omega t)},$$
using complex…
CherryGot
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16
votes
5 answers
Why do physicists use plane waves so much?
When looking at solutions of the Dirac equation people tend to give solutions as $$\psi^{(1)} = e^{\frac{-imc^2t}{\hbar}}\begin{pmatrix}1\\0\\0\\0\\\end{pmatrix},\psi^{(2)} =…
Ryan Parikh
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16
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6 answers
Popular depictions of electromagnetic wave: is there an error?
Here are some depictions of electromagnetic wave, similar to the depictions in other places:
Isn't there an error? It is logical to presume that the electric field should have maximum when magnetic field is at zero and vise versa, so that there…
Anixx
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14
votes
4 answers
According to Maxwell Equations, how does the light travel straight line?
According to Faraday's law of induction and Ampere's law, a changing magnetic field causes curl of electric field simultaneously; and also a changing electric field causes curl of magnetic field simultaneously. By combining these equations, the…
Tolga
- 143
14
votes
4 answers
Why are EM plane waves transverse?
I was reading Griffiths' Introduction to Electrodynamics, specifically Section 9.2.2 on plane waves. I can see that if we want a transverse wave traveling in the $z$ direction that we are only going to want our waves to have $x$ and $y$ components,…
user1236
- 561
12
votes
3 answers
Sinusoidal to complex form of wave equation
I know that a sinusoidal plane wave can be represented by the wave equation
$$ \psi (x,t)=A\, \cos(kx-\omega t) $$
I have also seen that a plane wave can be represented in complex exponential form as
$$ \psi (x,t)=A\, e^{i(kx-\omega t)} $$
I know…
K Ferreira
- 463
7
votes
1 answer
Incoming and Outgoing Waves in Quantum Field Theory
I apologize if this seems like a simple question, but I have been agonizing over it recently. In nonrelativistic quantum mechanics, a plane wave of the form $e^{\pm i\vec p\cdot \vec x}$ is called outgoing (incoming for the minus sign). However, in…
Daniel Waters
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6
votes
3 answers
Why don't plane waves always expand according to Huygens' principle?
I have seen a few videos about Huygens' principle and I don't understand why a plane wavefront doesn't expand both vertically and horisontally. According to my understanding of Huygens' principle, each point of the wavefront forms a "centre of…
Hajen1000
- 61
6
votes
2 answers
Understanding the wave equation in 3dimensions
I am learning about waves and the wave equation in lectures, and there was something interesting my lecturer said which I have not been able to find about online or in a book.
With regards to the three dimensional wave equation
$$
\frac{\partial^2…
Meep
- 4,167
6
votes
3 answers
The ubiquitous Planewave Ansatz
In physics, the planewave ansatz (meaning: an educated solution guess) is very ubiquitously used, when solving differential equations, in different domains of physics. E.g. to solve the dispersion relation of magnons or phonons in solids, also very…
user929304
- 4,910
5
votes
2 answers
Omitting the negative exponential in the plane-wave solution of the Schrodinger equation
The time-independent Schrödinger equation in one dimension for a free particle,
$$\frac{-\hbar^{2}}{2 m} \frac{\partial^{2} \Psi(x)}{\partial x^{2}}=\varepsilon\Psi(x)$$
can be solved as a homogeneous second-order linear ODE with constant…
Invenietis
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5
votes
1 answer
What is the logic behind box normalization and periodic boundary condition?
Free particle energy eigenfunctions are $A\exp{[i(Et-\textbf{p}\cdot\textbf{r})/\hbar]}$ are non-normalizable. To normalize them one introduces a procedure called 'box normalization' where one imposes periodic boundary condition (PBC). But isn't…
SRS
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5
votes
3 answers
Why is there a 90˚ phase angle between particle velocity and sound pressure in spherical waves?
My text says that in a plane sound wave (or in the far field), particle velocity and pressure is in phase. As we move closer to the sound source (to near field and more spherical waves), the phase angle between these two quantities will gradually…
jodles
- 151
4
votes
1 answer
Is the wave 4-vector a vector in general relativity?
For a plane wave $f(x)=A\cos(\omega t-{\bf{k\cdot x}})$, the wave $4$-vector in special relativity is $$k^\mu=(\omega,{\bf{k}}) .$$
This is a $4$-vector in special relativity, as can be seen by checking how it transforms under a Lorentz…
Khun Chang
- 639
4
votes
2 answers
Definition of complex permittivity
I'm not sure if this is the appropriate forum for my question as I actually am studying this as part of electrical engineering and I don't actually study physics. Nonetheless, I shall ask and if need be, move my question to another venue.
My…
user26869
- 153