Perpendicular component notation

In summary, if I have e^{i \mathbf{q_\perp \cdot x}} what does it mean?Specifically what does the \mathbf{q_\perp} mean?The equation I'm dealing with which contains this term is e^{i \mathbf{q_\perp \cdot x}}=\frac{i}{q_z} \int d^2 \mathbf{x} e^{i \mathbf{q_\bot \cdot x}}[\epsilon_2 e^{iq_z[H+h_2(\mathbf{x})]} - \epsilon_1 e^{iq_z h
  • #1
MadMax
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0
If I have [tex]e^{i \mathbf{q_\perp \cdot x}}[/tex] what does it mean?Specifically what does the [tex]\mathbf{q_\perp}[/tex] mean?

thanks
 
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  • #2
It usually means the perpendicular component of q relative to something.
 
  • #3
Yes that's what I thought. Relative to what though?

Surely it can't mean relative to x because the dot product would imply that the term always = 0 right?
 
  • #4
How could I guess 'relative to what'? I'd agree it's probably not x.
 
  • #5
The equation I'm dealing with which contains this term is

[tex]\epsilon(\mathbf{r})=\frac{i}{q_z} \int d^2 \mathbf{x} e^{i \mathbf{q_\bot \cdot x}}[\epsilon_2 e^{iq_z[H+h_2(\mathbf{x})]} - \epsilon_1 e^{iq_z h_1(\mathbf{x})}][/tex]

I guess it could be perpendicular to r... but what difference would that make? What would it mean?
 
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  • #6
It's probably perpendicular to the magnetic field intensity vector H.
 
  • #7
ahh see the H actually stands for height in this equation. :P h_x is a length also and purely a function of x.

But hmm perpendicular to H you say... that actually makes a lot more sense to me than any of the other variables if H were a vector, unfortunately its a mean separation, so that couldn't be it could it? I mean H is measured in a particular direction but... can you use that perpendicular symbol relative to something that's not a vector but measured in a particular dimension?

Cheers
 
  • #8
well thinking about it this is a 2 D problem using a radial or cartesian coordinate system. The radial dimensions are expressed by r and the cartesian dimensions are expressed by x= x_x + x_z.

Saying that we are dealing with something perpendicular to r makes no sense to me in the context of the system to be honest. Since it has cartesian symmetry but no radial symmetry. Although I could be missing somthing since the equation comes from a Fourier tranformation which I don't actually understand...

(a Fourier transform of the system

[tex]\epsilon(i f, r) = \epsilon_2(i f)[/tex] when [tex]H + h_2(x) \leq z < + \infty[/tex]
[tex]\epsilon(i f, r) = 0[/tex] when [tex]h_1(x) < z < H + h_2(x)[/tex]
[tex]\epsilon(i f, r) = \epsilon_1(i f)[/tex] when [tex]- \infty < z \leq h_1(x)[/tex]

)


Saying its perpendicular to x is pointless. So I'm inclined to believe its either perpendicular to x_x or x_z. But which I don't know... :/ Nah actually though I bet if I actually understood the Fourier transform I'd understand what that q is perpendicular to :/ Can anyone help please? :(
 
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1. What is perpendicular component notation?

Perpendicular component notation is a mathematical notation used to represent the components of a vector in a given direction that is perpendicular to the vector. It is typically denoted by a subscript symbol, such as "x" or "y", to indicate the direction of the component.

2. How is perpendicular component notation used in physics?

In physics, perpendicular component notation is commonly used to represent the forces acting on an object in a specific direction. For example, the force of gravity can be broken down into its perpendicular components, such as the x and y components, to better understand its effects on an object.

3. What are the benefits of using perpendicular component notation?

One of the main benefits of using perpendicular component notation is that it allows for a more clear and concise representation of vector components. It also makes it easier to perform calculations involving vector components, such as finding the magnitude and direction of a vector.

4. How is perpendicular component notation different from other vector notations?

Unlike other vector notations, such as unit vector notation, perpendicular component notation specifically represents the components of a vector in a direction that is perpendicular to the vector. This can be useful when dealing with vectors that have multiple components and allows for a more simplified representation.

5. Can perpendicular component notation be used for any type of vector?

Yes, perpendicular component notation can be used for any type of vector, including both two-dimensional and three-dimensional vectors. It is a versatile notation that can be applied to various fields of science and mathematics.

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