 |
Web Hosting by Netfirms | Free Domain Names by Netfirms |
|
|
|
|
Link to thread of next article. The deBroglie wavelength of weakly bound molecule? Date: 1996/01/10
Consider two particles bound to form a system (say a proton and neutron, or two hydrogen atoms, or quark and anti-quark). Assume that the coupling between the particles can be adjusted so that we can reduce the coupling strength to almost zero. Question. How does the wave-length of such a system vary as one reduces the coupling to the point that the two particles are no longer bound to form the system? One could imagine that in scattering experiments at energies much smaller then the coupling strength the two particles would act as one object, with a wavelength of lamda = h/mv where m is the mass of the system. As scattering energies approached the energy needed to bust the system apart, the wave-length might not be well defined. I'm sure there is stuff written on this, any help?
Re: The deBroglie wavelength of weakly bound molecule? Date: 1996/01/17
In article <4dhdlh$co6@ds8.scri.fsu.edu> jac@ds8.scri.fsu.edu (Jim Carr) writes:
> In article <4cvkc0$1m8r@hearst.cac.psu.edu> ale2@psu.edu (ale2) writes: > > > >Consider two particles bound to form a system (say a proton and > >neutron, or two hydrogen atoms, or quark and anti-quark). Assume that > >the coupling between the particles can be adjusted so that we can > >reduce the coupling strength to almost zero. > > Sorry for putting this off, but my first read of your question made > me think it was about the physics of resonances, a complicated subject. > > If you are willing to change systems, you can get pretty much whatever > you like, including using alpha emitters that are, in a technical > sense, not really bound at all - just well confined. It is even > more interesting to look at many-body systems like Be-8, which is > particle unstable but supports 'resonances', states that can be > quite narrow and long lived but which are not bound. You can see > them even in simple square-well QM calculations. What you notice > is that the wavefunction is 'free' but it gets piled up in the > potential so that a particle can get trapped there for quite a time. > > But this is not what you were asking, as I now understand your query. >
Thanks for considering my question. I should of stated my reason for the question, which i will do now. If one thinks of a pair of particles in a way that deBroglie might have then with two particles we have two "clocks" which combine to """"beat space"""", the doubling of frequency which halves the wavelength of the system. However this is done, the beating of space, it seems that the two particles must do this together in a coordinated manner (the beating of space), so as to double the frequency. Now one might think this synchronizing of the two particle system is disturbed when the two particle system interacts with other systems. This is where i think things might get interesting, if the wavelength is determined by in phase action, then interactions must disturb the in phase action and therefore disturb the wavelength.
I am sorry if this is stupid, I don't want to waste anyones time, just looking for conversation which might lead to ideas.
Thanks for your time and ideas, ale2@psu.edu
> > Question. How does the > >wave-length of such a system vary as one reduces the coupling to the > >point that the two particles are no longer bound to form the system? > > The wavefunction of the manybody system, that is, of the particles > relative to the center of mass, changes dramatically. Even a bound > state like the deuteron (H-2) is very diffuse with the proton and > neutron very likely to be several fm apart. > > However, the DeBroglie wavelength of the composite does not change > until it ceases to be treatable as a single entity. For example:
Two vibrating strings and the minimum area between them. Date: 1996/01/12
Consider the modes of the following system. Anchor two strings to the same two end points, but with possibly different tensions. Imagine the strings able to move independent of each other, that is they can pass through each other. As the strings can move independent of each other we will have two independent sets of modes, one for each string. But now change the problem a little. Let the minimum area defined by the two strings be proportional to a potential energy term of the two string system. So now the potential energy of the string system will be of two types, energy from stretching strings and energy from area between strings.
Consider the energy spectrum which results from varying the following,
For a different problem let the differential potential energy between the strings at some z be equal to (for strings attached to the two points in Cartesian coordinates (x,y,z)=(0,0,0) and (0,0,L)):
The bi-rubber vibrating thing. Date: 1996/01/10
Please consider the following. Let space be occupied simultaneously by two types of rubber, say real rubber and imaginary rubber. In equilibrium the real rubber and imaginary rubber have equal densities and are to be connected to each other in the following way. Let the real and imaginary rubber be divided up into very small volumes. The small volumes of real rubber and imaginary rubber which occupy the same region of space in equilibrium are tied together at their centers with a piece of elastic thread. This is impossible to do but easy to imagine. One must imagine that each small region of space consists of three things , a small volume of real rubber, a small volume of imaginary rubber, and elastic thread. There are two ways the rubbers can vibrate, vibrations in which the elastic threads don't stretch and vibrations in which the threads do stretch. Consider the various types of free oscillations and driven oscillations of this system.
A vibrating sphere, curvature, "flow" of curvature. Date: 1996/08/02
The integral of dA*(surface curvature) over any size smooth sphere is 4Pi? This is in a sense easy to see, a small sphere has high curvature which is balanced by its small area, whereas a large sphere has the opposite qualities. Now an interesting thing about the total curvature of a sphere is the fact? that if the sphere is deformed in a "smooth" way the total curvature does not change! Now consider the following thought experiment.
Consider the vibrational mode of a sphere which can be excited by squeezing the sphere between two flat plates and then suddenly releasing the sphere. It will give off gravitational radiation because it has changing quadrapole to sphere to quadrapole' to sphere to quadrapole to ..... shape?
Now as the total curvature over this vibrating sphere is constant one can watch the sphere vibrate and at the same time (with a little imagination) watch the curvature "flow" across the surface of the sphere. The flow is from the poles to the equator and then back to the poles.
The modes of two superimposed balls and the volume between. Date: 1996/01/22
Imagine two basketballs, call them ying and yang, which can occupy the same space but which have no interactions. As they are separate we will have two separate modes of vibration, one for each basketball. Now let the volume contained between both surfaces be proportional to potential energy for the two ball system. The energy for the system will be:
kinetic energy of each ball(rotation and radial motion) + potential energy of stretched ball rubber + potential energy of volume between balls.
Please consider two modes of vibration.
1) with the system at rest, give the ball named ying a compressive impulse inward, the ball yang will follow ying.
2) with the system at rest, give the ball named yang a compressive impulse inward, the ball ying will follow yang.
For more fun, let the differential potential energy between balls go as:
(a constant)*(distance between dA ying and dA yang to some power)
where dA is a small area, and the distance between dA ying and dA yang is zero in equilibrium.
Pulley rubber band array that mimics fibber bundles? Date: 1996/06/11
Imagine a long and narrow plane covered by a rectangular array of coplanner pulleys, each pulley of which has four groves. Let each pulley be connected to nearest neighbors by means of rubber bands, pulleys along the edge will be connected to only 3 neighbors, and pulleys at a corner will be connected to only 2 neighbors. Imagine the whole system of pulleys and rubber bands is lossless, if i turn one pulley every other pulley in the array will turn in the same direction with no work done. With this done make a mark on the circumference of each pulley at the same spot relative to the array. So in equilibrium, all pulleys "point" in the same direction (have the same angle theta.)
Now lock the rotation of the pulleys along one of the narrow edges of the rectangle and give the pulleys on the opposing side of the rectangle a rotation of measure alpha, because of the rubber bands work will be done in doing this. Now imagine pulleys on these opposing edges are connected together by chains (edge pulleys each have an additional chain sprocket) so that in a sense opposing edges are identified.
With this done, does anyone smell fiber bundles?
What is neat is the energy of the system is invariant under a rotation of each pulley by the same angle. While potential energy shows up by a relative difference in phase between neighboring pulleys.
For more fun try making these arrays on the surface of a large sphere or torus or cylinder. Imagine the different "motions" of such a system.
Homework, come up with a 3D mechanical analog.
Thanks for useful conversation with ccb104@psuvm.psu.edu about this matter :)
References _Particle Physics, A Los Alomos Primer_ page 35.
Re: quick question about photons... Date: 1996/01/22
In article <ragnaroek1996Jan19.231835.17382@news2.compulink.com> falstaff@idirect.com (Dan Siegal) writes:
> My question is a simple one and may seem to some of you an almost > ridiculous one. I am going to ask it anyway? > > How many electrons are in one photon? Is it Avogadro's number or what? >
The photon seems neutral, so it must be equal quantities of positive and negative charge. imagine a double strand of DNA with each strand being of one type of charge. now imagine this thing going past you and imagine the fields. the distance between strands must be incredibly small so as to make the existence of such an idea unprovable.
Re: quick question about photons... Date: 1996/01/23
In article <HFRANZ.96Jan23111058@acds02.physik.rwth-aachen.de> hfranz@acds02.physik.rwth-aachen.de (Holger Franz ) writes:
> -----BEGIN PGP SIGNED MESSAGE----- > > >>>>> Regarding Re: quick question about photons...; ale2@psu.edu (ale2) adds: > > ale2> In article <ragnaroek1996Jan19.231835.17382@news2.compulink.com> > ale2> falstaff@idirect.com (Dan Siegal) writes: > > >> My question is a simple one and may seem to some of you an almost > >> ridiculous one. I am going to ask it anyway? > >> > >> How many electrons are in one photon? Is it Avogadro's number or > >> what? > >> > > ale2> The photon seems neutral, so it must be equal quantities of > ale2> positive and negative charge. imagine a double strand of DNA > ale2> with each strand being of one type of charge. now imagine this > ale2> thing going past you and imagine the fields. the distance > ale2> between strands must be incredibly small so as to make the > ale2> existence of such an idea unprovable. > > Good heavens! How could a macroscopic structure like a DNA make up a > photon? This is ridiculous. > sorry for the confusion. imagine the positive and negative charge densities are in the shape of a double helix, with positive charge for one helix and negative charge for the other helix. but you are right, this is ridiculous =)
|
