| T.R | Title | User | Personal
Name | Date | Lines |
|---|
| 747.1 | More than one nu here | CAADC::MARSH | Jeffrey Marsh, DTN 474-5739 | Sun Aug 09 1987 04:29 | 13 |
| A monochromatic beam of light is composed of particles (photons) each of which
has energy E=h*nu where nu is the frequency of light. The more intense the
beam, the more photons you have.
A single photon has associated with it a probability density function
Phi(x,y,z,t) which describes the probability of finding the photon at
position and time (x,y,z,t). (The probability density is Phi times its
complex conjugate.) You can Fourier-decompose Phi into pure frequencies.
If the photon's position is known exactly then this decomposition cotains
all frequencies.
The important thing is not to confuse these frequencies with the frequency
of the light -- they are distinct quantities.
|
| 747.2 | | ENGINE::ROTH | | Mon Aug 10 1987 11:38 | 35 |
| 747.3 | | ENGINE::ROTH | | Mon Aug 10 1987 11:48 | 15 |
| In looking at .1, the 'frequencies' mentioned in relation to the
position are really the particle momentum; formally position and
momentum play the role of time and frequency in the Fourier transforms
that relate them.
There is another 'frequency' also - in an atom the wave equation has
spherical harmonics as solutions, which are an interesting example of
harmonics existing over a non-commutative group (the group of orientations
of a sphere). The Fourier transforms one is used to are over the group
of translations along a line, and are particularly simple as a result -
but you can do all the usual stuff like convolution and transforations
if you well-define your integrals over any continuous group, (the so-called
Lie groups).
- Jim
|
| 747.4 | getting there, I think, but still a bit befuddled | EAGLE1::BEST | R D Best, Systems architecture, I/O | Tue Aug 11 1987 19:20 | 32 |
| re .1:
>A monochromatic beam of light is composed of particles (photons) each of which
>has energy E=h*nu where nu is the frequency of light.
Does this mean that nu is a macroscopic parameter associated with the beam
that bears no direct relation to the wave function of the particle ?
I'm still a bit confused. What do we mean when we say 'a beam of light
has such-and-so a frequency' ?
>A single photon has associated with it a probability density function
>Phi(x,y,z,t) which describes the probability of finding the photon at
>position and time (x,y,z,t). (The probability density is Phi times its
>complex conjugate.) You can Fourier-decompose Phi into pure frequencies.
>If the photon's position is known exactly then this decomposition cotains
>all frequencies.
OK, but this is not nu, right? Nu has to do with the macroscopic frequency,
right ?
>The important thing is not to confuse these frequencies with the frequency
>of the light -- they are distinct quantities.
OK, but do they bear some relationship to one another ? For example, is the
macroscopic frequency measured something like the the modulating frequency
for the photon packet ? My model here is that the photon can be viewed
(at a single point in time) as something like a Gaussian envelope modulated
by some frequency (call it f0). That modulating frequency (f0) would be
the macroscopic frequency we measure, even though the signal has Fourier
frequency components splashed around f0.
Did I get it right ?
|
| 747.5 | Aha! | EAGLE1::BEST | R D Best, Systems architecture, I/O | Tue Aug 11 1987 19:37 | 4 |
| re .2:
Aha! sorry about .4; I wrote it before I read .2. This answers my question.
Thanks.
|