Science > Physics > I am puzzled by several questions of quantum mechanics.
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Science > Physics |
| User: |
"dijkstra" |
| Date: |
16 Oct 2006 08:42:14 AM |
| Object: |
I am puzzled by several questions of quantum mechanics. |
First One:If I want to express a photon in the laevorotary state in
plane polarization representation, then how?
But I don't know what the two eigenstates are.
Second One: Don't use euqation but calculate the probability of a
harmonic oscillator staying at any position. The oscillation is
described as x = Asinwt.
Can anyone guset a formulation with an reasonable reason(can be not
very strict).
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| User: "Sorcerer" |
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| Title: Re: I am puzzled by several questions of quantum mechanics. |
16 Oct 2006 10:23:23 AM |
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"dijkstra" <chossing@gmail.com> wrote in message
news:1161006134.410401.281070@i42g2000cwa.googlegroups.com...
| First One:If I want to express a photon in the laevorotary state in
| plane polarization representation, then how?
First flush the lavatory or the lavae will pupate.
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| User: "dijkstra" |
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| Title: Re: I am puzzled by several questions of quantum mechanics. |
16 Oct 2006 09:19:42 AM |
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For the second question I mean don't apply Schr=F6dinger equation
..Thanks.
dijkstra wrote:
First One:If I want to express a photon in the laevorotary state in
plane polarization representation, then how?
But I don't know what the two eigenstates are.
Second One: Don't use euqation but calculate the probability of a
harmonic oscillator staying at any position. The oscillation is
described as x =3D Asinwt.
Can anyone guset a formulation with an reasonable reason(can be not
very strict).
.
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| User: "Timo A. Nieminen" |
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| Title: Re: I am puzzled by several questions of quantum mechanics. |
16 Oct 2006 03:34:04 PM |
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On Mon, 16 Oct 2006, dijkstra wrote:
If I want to express a photon in the laevorotary state in
plane polarization representation, then how?
But I don't know what the two eigenstates are.
One usually just writes a|H> + b|V> to give any arbitrary polarisation
state for a plane wave (or paraxial beam mode). |H> is the plane wave
with electric field horizontal, |V> with it vertical. Propagation is
horizontal. You can write down what the electric and magnetic fields are
if you want, but it usually doesn't matter.
If a and b have the same complex phase angle (eg both real), you have
plane polarisation at some angle depending on the relative magnitudes of a
and b. If |a| = |b|, 45 degrees.
If a and b are pi/2 out of phase (eg a real, b purely imaginary), and
|a|=|b|, you have circular polarisation.
As for which is laevo and which is dextro, be warned that there is no
universal convention. Check what is used in your field. What I call
left-handed has positive angular momentum (ie spin vector and wavevector
are parallel; right-handed is anti-parallel).
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
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| User: "" |
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| Title: Re: I am puzzled by several questions of quantum mechanics. |
16 Oct 2006 12:18:32 PM |
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dijkstra wrote:
First One:If I want to express a photon in the laevorotary state in
plane polarization representation, then how?
You are going to need to get yourself an introductory quantum
text first. Plus you are going to have to read it, and do all the
homework questions in it.
Then you are going to have to get yourself a couple intermediate
QM texts, read them, and do all the homework questions in them.
Then you can get to photons.
But I don't know what the two eigenstates are.
Second One: Don't use euqation but calculate the probability of a
harmonic oscillator staying at any position. The oscillation is
described as x = Asinwt.
Can anyone guset a formulation with an reasonable reason(can be not
very strict).
The probability of finding a SHO in any given location goes like so.
P(x) dx
You get the prob of finding the particle at x to x + dx. You can work
this out from one period of its oscillation, and by the time it spends
in that region. So, you know the formula for motion, you need to
know from that the time it spends in x to x + dx as a function of x.
But to go from x to x + dx takes dt = dx / V(x). And you need
your result to be normalized such the probability of the particle
being someplace is 1.
If that's not enough hint for you, you probably should not be
studying this.
Socks
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| User: "Greg Hansen" |
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| Title: Re: I am puzzled by several questions of quantum mechanics. |
16 Oct 2006 07:41:41 PM |
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dijkstra wrote:
First One:If I want to express a photon in the laevorotary state in
plane polarization representation, then how?
But I don't know what the two eigenstates are.
Momentum eigenstates are plane waves, and they can be polarized in one
direction or the other. So far it's no different than the classical
field. But the quantum field follows deBroglie's relation, so the
momentum of the field goes in steps of h/lambda. The occupation number
formalism is usually used to track the number of steps that are in each
wavelength.
Second One: Don't use euqation but calculate the probability of a
harmonic oscillator staying at any position. The oscillation is
described as x = Asinwt.
Can anyone guset a formulation with an reasonable reason(can be not
very strict).
Easy: zero. By the uncertainty principle, as the position is confined
to a smaller region, the momentum gets larger and it's not going to stay
where you put it.
To be a little fancier, like supposing the position has a Gaussian
distribution with width w about point x, and then asking how the
probability distribution evolves over time, you need to solve
Schroedinger's equation.
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| User: "dijkstra" |
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| Title: Re: I am puzzled by several questions of quantum mechanics. |
17 Oct 2006 11:55:23 PM |
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For the first question I am sorry for my ignorance. But the answer of
the second question is P=1 (when x=Acoswt);
0 (when other position).
It has nothing to do with quatum mechanics. It should be noted that it
does not mean to calculate the probability at any position(it is zero
obviously) but at the neighborhood of that position.
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