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Topic: Momentum space

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In the News (Wed 22 May 19)

  Angular momentum - Wikipedia, the free encyclopedia
In physics the angular momentum of an object with respect to a reference point is a measure for the extent to which, and the direction in which, the object rotates about the reference point.
The reason angular momentum is important in physics is that it is a conserved quantity: a system's angular momentum stays constant unless an external torque acts on it.
Under this formalism, angular momentum is the 2-form Noether charge associated with rotational invariance (As a result, angular momentum isn't conserved for general curved spacetimes, unless it happens to be asymptotically rotationally invariant).
en.wikipedia.org /wiki/Angular_momentum   (1467 words)

 Space Elevator: Momentum Building
Anchored in space a ribbon 62,000 miles (100,000 kilometers) long would be made of carbon nanotubes.
He is a leading authority on the space elevator concept, and is moderator for this week’s event.
Edwards is quick to run down what’s up on the space elevator challenges, from carbon nanotube technology, power beaming, climber hardware to space debris impacts on the ribbon, health and safety issues, as well as cost, politics and regulations.
www.space.com /businesstechnology/space_elevator_040629.html   (793 words)

 Wavefunction - Wikipedia, the free encyclopedia
An element of a vector space can be expressed in different bases; the same applies to wave functions.
The wavefunction for a one dimensional particle in momentum space is a complex function
An example of this is the spacial wavefunction associated with a particle in one dimension which expands the state of the particle in terms of states with definite position.
en.wikipedia.org /wiki/Wavefunction   (1100 words)

 Istria on the Internet - Prominent Istrians - Paolo Budinich
Space time and momentum space appear then as conformally dual, that is conjugate with respect to conformal reflections.
It is conjectured that space-time and momentum space may be both conformally compactified and correlated by conformal inversion, rendering a priori impossible the empirical realization of the concept of both infinity and infinitesimal.
We consider the global structure of momentum space PI3,1 in a field theory which is covariant with respect to the action of global conformal group G. We show that PI3,1 is a homogeneous space for G which coincides with (S3 x S1)/Z2 compact space.
www.istrianet.org /istria/illustri/budinich/abstracts.htm   (3961 words)

When momentum is discussed, the preference in the future is for it's meaning to be what is termed here as total momentum.
All momentum is physically the same is all dimensions, hyper and normal macro spaces.
Momentum is free to change vectors freely when the dimension it is traveling in becomes as small or smaller than the next smaller space.
home.att.net /~bob.rutkiewicz/Nomencl.htm   (1070 words)

 Momentum-Exchange Tethers
is a long thin cable used to couple two objects in space together so that one transfers momentum and energy to the other.
It could be used to "catch" a payload coming from any given direction (in its plane of rotation) at any given speed (less than its maximum tip speed), and then some time later, "launch" the payload off in some other direction at some other speed.
To reach the surface of the planet, the orbital altitude should be equal to half the length of the rotating cable.
www.tethers.com /MXTethers.html   (708 words)

 Uncertainty versus duality
The momentum and the position of a particle cannot be measured simultaneously with arbitrarily high precision.
Thus the particles momentum is disturbed during the measurement of the position.
A transversal momentum transfer would not change merely the uncertainity of momentum namely the average spread around the mean value of the momentum but the mean value (or the expectation value as it is called in quantum mechanics)of the transversal momentum itself.
physics-qa.com /html/kqm09.htm   (1782 words)

 RedOrbit - Technology - Flying in the Face of Uncertainty: Human Risk in Space Activities
This momentum is evident in the renewed emphasis on human exploration of the moon and Mars.
The most prominent space activities that represent the range of risks to first and third parties and the spectrum of risks from private and government space projects are human space exploration, space tourism, planetary protection, and space transportation.
Because of the dangers of ascent and re-entry, because of the hostility of the space environment, and because we are still relative newcomers to this realm, operation of the shuttle and indeed all human spaceflight must be viewed as a developmental activity.
www.redorbit.com /news/display?id=169410&source=r_technology   (4629 words)

 Feng Wang's Personal Page
In the conventional coordinate space, however, the energy insensitive properties such as anisotropic (angular dependent) properties and chemical bonding mechanisms, are challenges to design new and sensitive experimental means for their observation.
Electron momentum spectroscopy (EMS) in conjuction with momentum space quantum mechanics is able to reveal additional informaton to study orbitals and chemical bonding mechanisms of molecules [10-11].
Because in coordinate space, the information is sensitive when energy is involved but insensitive when orbitals are in the equivalent positions in the space, whereas in momentum space, the information such as equivalent positions in space which cause energy degenerate states and "invisible" in coordinate space could be significant.
www.it.swin.edu.au /personal/fwang/Mom/Mom_butane.html   (1465 words)

 Space Drive
Conservation of momentum requires that the momentum imparted to the vehicle must be equal and opposite to the momentum imparted to a reaction mass.
By displacing them in space, the reactant is shifted to a point where the field has a slope, thus producing reaction forces between the source and the reactant.
Simply put, a space drive requires some controllable and sustainable means to create asymmetric forces on the vehicle without expelling a reaction mass, and some means to satisfy conservation laws in the process.
www.zamandayolculuk.com /cetinbal/SPACEDRIVE.HTM   (5369 words)

 Physics Help and Math Help - Physics Forums - View Single Post - Momentum space and position space
It seems to treat "momentum" and "position" as two basises in that both can span the complete Hilbert space and a unitary tranformation is used to translate the two basis.
I vision now the Hilbert space can be constructed with a intertwining "momentum" and "position" not exactly as a direct sum or product; they might not be orthogonal to each others but either one will not be able to span the whole Hilbert space.
I guess what troubles you is the fact that in classical mechanics, the phase space (p,q) is the state space, while in quantum theory, only one of both (q or p or a mixture) seems to be necessary.
www.physicsforums.com /showpost.php?p=279738&postcount=3   (323 words)

 physics momentum -- physics momentum   (Site not responding. Last check: 2007-10-23)
Angular Momentum Angular momentum is a measure of the tendency of an object to keep rotating, or moving in a circle.
Definition of Momentum In physics, momentum is a physical quantity related to the velocity and mass of an object.
Momentum (generally abbreviated as P) is defined to be the mass of an object multiplied by the...
www.aratom.com /physicsmomentum   (3361 words)

 Dewey Redman / Cecil Taylor / Elvin Jones - Momentum Space
Momentum Space, commissioned by The Creative Music Institute, is a collection of trios, duets, and solos, that creates a powerful musical statement.
Elvin Jones, primarily known as the driving rhythmic force in the great John Coltrane quartet with McCoy Tyner and Jimmy Garrison, is also unquestionably one of the most influential percussionists of all time.
The music on Momentum Space, though admittedly not for the casual listener, is ripe with buoyant and accessible passages, that will surprise and delight those who take the journey.
jazzusa.com /stories/momentumspace.asp   (144 words)

 success.html   (Site not responding. Last check: 2007-10-23)
The conjugate point is a region of total time dilation and hence when this photon is absorbed (and experiment indicates photons collide spherically) by a deuteron the time dilation is sufficiently extreme to ionize the atom by strongly repelling any associated electrons in the region according to the 'General Case'.
Simultaneously the physical extent of the extreme time dilation will cause two adjacent deuterium nuclei to overlap in a common momentum space because they obtain to a state where they have a common de Broglie wavelength which is greater than or equal to the interparticle distance.
Increasing the number of particles at some point increases the average number of particles which will be in a particular momentum space so that at some point we have seen the evolution of a finite number, k, of momentum spaces each of which is occupied by average number, j, of particles so that j*k= n.
www.singtech.com /success.html   (1971 words)

 Re: Gauge Transformations in Momentum Space?
The probability of finding definite momentum particle in each finite volume W is W/V, which is "zero".
After all, the number of points in 3D space is not countable, and one can associate a distinct basis vector (eigenvector of the position operator) with each such point.
In this approach, the numbers like 1/sqrt(V), where V is the volume of the entire space, make perfect sense, and there is no trouble to calculate the integral Integral dx 1/sqrt(V) exp(ipx)^2 = 1 even if the integrand is "zero" everywhere.
www.lns.cornell.edu /spr/2005-10/msg0071721.html   (1007 words)

 Space - - Momentum continues to build in European space sector
In the wake of last year’s wide-ranging Green Paper consultation and the subsequent White Paper on European Space Policy, the European Union and its partners are moving forward with important new space initiatives.
As the citizens of a newly enlarged Europe look to the future, fresh initiatives in the space sector are broadening the role of co-operation and tackling new and important challenges.
An important element of the Agreement entails the convening of an EC/ESA ‘High-Level Space Policy Group’, gathering representatives from EU and ESA Member States with the goal of reaching a common understanding on the implementation of European Space Policy, in particular the preparation of the future European Space Programme.
ec.europa.eu /comm/space/news/article_1222_en.html   (709 words)

 Simplified Road Map to Reciprocal Space:
This point is called the center of the experiment and labeled C. The origin of inverse space is the point where the incident unit vector ends.
In addition to giving a qualitative impression of the source of a diffraction pattern, another major use is in relating the momentum change of the incident x-ray photon to the diffraction experiment.
is often called the momentum change vector and inverse space is sometimes called momentum space.
www.eng.uc.edu /~gbeaucag/Classes/XRD/ReciprocalRoadMap.html   (960 words)

 Field theory in superfluid 3He: What are the lessons for particle physics, gravity, and high-temperature ...
on the two-dimensional surface in the momentum space is preserved,
The spin makes a hedgehog in the momentum space, which is topologically stable.
The topology of the propagator in the four-dimensional momentum space is thus essential for the Landau theory of an interacting
www.pnas.org /cgi/content/full/96/11/6042   (3620 words)

 Space and momentum representation
Part 2: The (idealized) reprentations of states of physical systems by using either space or momentum dependent functions are often useful in practice, good for the imagination and easy and mnemonic to handle.
We will restrict this chapter to one space coordinate, no fuss to translate it to more space dimensions for the reader.
In the ordinar space-vector space we have analogously
physnet.physik.uni-oldenburg.de /~hilf/lehre/QM/QM/node16.html   (237 words)

 Perfect localisation in momentum space   (Site not responding. Last check: 2007-10-23)
It is completely localised in k space, because it has compact support in k and its support is the
This state is the eigenstate of the wave number operator (5) because it consists of only one plane wave component.
which shows that it is also an idealised case because a real quantum particle can not spread into the whole space homogeneously in finite time.
www.kfki.hu /(iframe)/physics/physedu/schrodinger/freewp97/node11.html   (133 words)

 Space passenger senses momentum - Space News - MSNBC.com
The primary aim of the space mission was to deliver a fresh Soyuz escape capsule to the space station.
His health was monitored to study the effects of space flight, and he also sponsored an educational effort called “Hip to Be Square,” aimed at heightening interest in math and science among South African students.
Because of his scientific and educational work, Shuttleworth maintained that he shouldn’t be considered a “space tourist.” His efforts turned skeptics into supporters, and on Monday he observed that the fruits of his flight were well received in South Africa.
www.msnbc.msn.com /id/3077958   (949 words)

 NASAexplores 9-12 Lesson: Momentum in Space (Student Sheets)
Space sailing, however, does not use the wind, but the sunlight pressure that is reflected off lightweight giant sails.
The spacecraft gains momentum in a continuous thrust that increases or decreases its orbital energy depending on which way the sail is tilted relative to the sunlight direction.
State the Law of Conservation of Momentum, and describe an example.
www.nasaexplores.com /show_912_student_st.php?id=021224123419   (380 words)

 Gauge Transformations in Momentum Space?
In the 2nd-quantized Fock\nandgt; space this means we\'re mixing some of the annihilation and creation\nandgt; operators - because they were defined in terms of the original +ve\nandgt; and -ve energy modes.
You can switch between position\nand momentum representations of wave functions, but quantum fields are\ncompletely different beasts (see recent thread "Why no tensors in\nquantum mechanics?").\n\nThe only point to introduce quantum fields Psi(x,t) in QFT is to have\nconvenient "building blocks" for the interacting Hamiltonian.\nThe gauge invariance of Psi(x,t) is a heuristic aid in this\nconstruction.
The\nandgt; wavefunction of the state with definite momentum is "zero"\neverywhere\nandgt; in the position space.
www.physicsforums.com /showthread.php?threadid=88751   (4852 words)

The operator splitting algorithm separates the Hamiltonian into a kinetic energy term and a potential energy term so that in position space potential energy is simple function and in momentum space the kinetic energy is easily calculated.
Therefore, when we initiate this plane wave in position space and transform it to momentum space, we expect to find only one value for momentum: k.
Where as the Visscher and the Crank-Nicholson grid space are flat with an infinite potential at each end, the operator splitting grid space is round so that the highest x value cell is the same as the lowest grid cell.
webphysics.davidson.edu /students/mecarroll/TDSE/crank-nicholson.htm   (676 words)

 Momentum Conservation in Space Science   (Site not responding. Last check: 2007-10-23)
Instead, in the absence of other forces expected in space, each piece maintained the same trajectory as each other piece (as shown in the artist's rendition below or the real images from the Hubble if you click on the image) up to their fiery end in Jupiter's atmosphere.
Space sciences also benefit enormously from Newton's Laws.
Calculate the effect of a slingshot encounter on a spacecraft approaching Jupiter in exercise 3-12.
dept.physics.upenn.edu /courses/gladney/mathphys/subsubsection3_1_3_2.html   (382 words)

 Radiation hydrodynamics in spherical symmetry
This equation derives from the space component of the four-divergence of the stress-energy tensor.
Once a 1+1 decomposition of space-time Arnowitt_Deser_Misner_62,Smarr_York_78 and a basis in the momentum phase space for the particle four-momentum have been chosen, the directional derivative along the phase flow can be expressed in terms of partial derivatives of the distribution function with respect to the space-time coordinates and momenta Lindquist_66,Mezzacappa_Matzner_89.
The integration of the Boltzmann equation over momentum space, spanned by the particle direction cosine and energy, gives the local conservation laws for particle number and energy.
www.cita.utoronto.ca /~liebend/transport/node4.html   (1250 words)

 Dreams of Space: The momentum and inertia of time
The space shuttle is the relic of an age at NASA marked by large dreams but few realizations.
Easy, cheap access to space is a great goal, but when that goal ends up in the most expensive (and dangerous) launch vehicle ever built, it's time to go back to the drawing board.
As it has been previously mentioned, the only people who seem to support the space shuttle are those whose wallets (or constituents) are affected by it.
www.lpl.arizona.edu /~darcher/space/2005/08/momentum-and-inertia-of-time.html   (682 words)

 Notation and terminology: phase space
Just as the three position coordinates (x, y, z) of a pointlike atom can be envisioned as a point in a 3-dimensional space, so also the 6N coordinates needed to describe N pointlike particles can be imagined as a single point in a 6N-dimensional space.
This 6N-dimensional space is known as phase space.
Since the position of the point in phase space fixes the 6N variables that comprise a complete microscopic description of the system, each point in phase space corresponds uniquely to a single state of the system, and vice versa: every allowed point in phase space corresponds to a state of the system.
users.wpi.edu /~phillies/stat4/node4.html   (364 words)

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