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Topic: Particle in a box

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	Schrodinger equation
		Assume the potential U(x) in the time-independent Schrodinger equation to be zero inside a one-dimensional box of length L and infinite outside the box.
		For a particle inside the box a free particle wavefunction is appropriate, but since the probability of finding the particle outside the box is zero, the wavefunction must go to zero at the walls.
		For the particle in a box with infinite walls, the probability must be equal to one for finding it within the box.
	hyperphysics.phy-astr.gsu.edu /hbase/quantum/pbox.html (214 words)

	Particle in a Box
		In this problem a particle of mass m is constrained to move along a line of length a.
		At the ends of the line are large potential energy barriers that keep the particle within the "box." In the quantum-mechanical treatment of the problem the Schrödinger wave equation is used to calculate the allowed energies of the particle.
		, in the "Box" is indicated by the presence of a plot of
	www.chm.davidson.edu /ronutt/che115/Box/Box.htm (0 words)

	Schrodinger equation
		The idealized situation of a particle in a box with infinitely high walls is an application of the Schrodinger equation which yields some insights into particle confinement.
		If a particle is confined into a rectangular volume, the same kind of process can be applied to a three-dimensional "particle in a box", and the same kind of energy contribution is made from each dimension.
		The ground state of a three-dimensional box of dimension L can be obtained by setting n=1 for all three dimensions, giving an energy three times the ground state energy of the one-dimensional box.
	hyperphysics.phy-astr.gsu.edu /hbase/quantum/schr.html (0 words)

	BBC - h2g2 - Quantum Mechanics - particle in a box (under construction)
		Quantum mechanics is a field that describes the behaviour of microscopic particles when they begin to behave like waves.
		Real particles move in 3 dimensions, but a simple example is the 1-dimensional 'particle in a box'.
		If n = 0, the function becomes sin(0) which is always 0, whether the particle is in the box or not.
	www.bbc.co.uk /dna/h2g2/A2658693 (0 words)

	Particle Flow Tools Box 3 Pro
		The Particle Flow Tools®: Box 3 Pro plug-in has been created to extend the capabilities of the build-in Particle Flow system in Autodesk® 3ds Max® with many new and sophisticated operators.
		Particle Flow Tools: Box 3 Pro is primarily a toolset for creating your own custom Particle Flow operators, although it does come with several exceptionally useful presets
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	www.ideateinc.com /products/multimedia/plugins/particle_flow_tools.html (274 words)

	One Dimensional Particle in a Box (Site not responding. Last check: )
		A 1-D PIAB is closely related to the Free Particle, the difference being that there are walls of infinite potential energy that contain the particle.
		Inside the box, we assign the potential energy to be 0, while outside it is infinite.
		Since the particle is viewed as "bouncing" back and forth between the two sides, the trig solutions (cos) are preferred, being associated with a standing wave inside the box.
	www.cobalt.chem.ucalgary.ca /ziegler/educmat/chm386/rudiment/models/piab1/piab1.htm (118 words)

	Particle in a box - RecipeFacts (Site not responding. Last check: )
		2.2 The particle in a 2-dimensional or 3-dimensional rectangular box
		See also the Particle in a spherically symmetric potential where the case is treated of a particle in a spherical box, or the particle in a ring which shows the case for a particle in a 1D ring.
		The particle in a 2-dimensional or 3-dimensional rectangular box
	www.recipeland.com /facts/Particle_in_a_box (2523 words)

	Particle in a box - Glasgledius (Site not responding. Last check: )
		The particle in a box (or the square well) is a simple idealized system that can be completely solved within quantum mechanics.
		As we shall see, the solution of the Schrödinger equation for the particle in a box problem reveals some decidedly quantum behavior of the particle that agrees with observation but contrasts sharply with the predictions of classical mechanics.
		For the case of the particle in a 1-dimensional box of length L, the potential is zero inside the box, but rises abruptly to infinity at x = 0 and x = L.
	www.glasglow.com /E2/pa/Particle_in_a_box.html (1494 words)

	Particle in a box
		The quantization of energy levels for the "particle in a box" problem is a consequence of Schroedinger's equation and the required properties of the wavefunctions.
		That means that the particle is so fast that its wavefunction adapts itself to the new size of the box nearly instantaneously (for all practical purposes), and at any time the wavefunction of the particle is a solution of the time-independent Schroedinger equation.
		When we reached the limit that the size of the box is infinitely large (relative to the particle), the energy levels are so close together to be indistinguishable from a continuous distribution, just as we would expect from a free particle.
	lofi.forum.physorg.com /Particle-in-a-box_7288.html (4135 words)

	NetLogo Models Library: GasLab Gas in a Box
		The basic principle of the models is that gas particles are assumed to have two elementary actions: they move and they collide - either with other particles or with any other objects such as walls.
		The particles are modeled as hard balls with no internal energy except that which is due to their motion.
		Particles are colored according to speed -- blue for slow (speed less than 5), green for medium (above 5 and below 15), and red for high speeds (above 15).
	ccl.northwestern.edu /netlogo/models/GasLabGasinaBox (1085 words)

	Particle In A Box
		A particle starts from one side of the box at zero amplitude, hits the opposite side of the box (also at zero amplitude) and must return to its starting point, continuing the pattern.
		Likewise, the energy of a particle, which depends on k, is also quantized for a particle in a box and continuous for an unbound free particle.
		The box is of length a along the x axis, length b along the y axis and length c along the z axis.
	physics.gmu.edu /~dmaria/590%20Web%20Page/public_html/qm_topics/potential/well/ParticleInABox.htm (1542 words)

	Orbits in Strongly Curved Spacetime
		Kepler's laws of planetary motion, grounded in Newton's theory of gravity, state that the orbit of a test particle around a massive object is an ellipse with one focus at the centre of the massive object.
		If the particle passes the energy peak and continues to lesser radii, toward the left, its fate is sealed--it will fall into the fl hole and be captured.
		With sufficient angular momentum, a particle can approach the event horizon as closely as it wishes (assuming it is small enough so it isn't torn apart by tidal forces), but it can never cross the event horizon and return.
	www.fourmilab.ch /gravitation/orbits (2354 words)

	outline, count,measure,Particle Characterization Software,AFM,SPM,Particle Analysis,nanoparticles
		A particle is defined as a surface entity which is spatially defined as an individual unit.
		As the name indicates, the key requirement for detecting particles is to set a proper threshold level in the Z scale.
		Particle Analysis Dialog Box: In the Particle Analysis Dialog Box, if the Threshold check box is selected, a defined threshold level is applied to the image.
	nanoparticles.pacificnano.com /particle-analysis-software.html (852 words)

	Bound States
		The simplest model of a bound state is known as the particle in a box: like a ball on a pool table, the electron feels zero force while in the interior, but when it reaches an edge it encounters a wall that pushes back inward on it with a large force.
		The "box" is actually just an empty cavity within a solid piece of silicon, amounting in volume to a few hundred atoms.
		The wave patterns must be zero at the ends of the box, because we are assuming the walls are impenetrable, and there should therefore be zero probability of finding the electron outside the box.
	www.vias.org /physics/bk6_04_04.html (679 words)

	particle in a box
		The plot on the left shows you the numerical solution to the Schrödinger Equation for a particle in a box of width W at the energy E. The left edge of the box coincides with the border of the plot, the right edge is given by the gray vertical bar on the right.
		As we know, the square of the wavefunction is proportional to the probability to find a particle at this location, which means that for this particular solution the probability would grow to infinity - which is impossible.
		Furthermore we know that the probability o find the particle outside of the box (to the right of the gray bar) is zero, after all it's supposed to be in the box...
	www.williams.edu /Chemistry/dbingemann/Chem153/particle.html (0 words)

	The Particle in a Box
		The highest probability to find the particle in the box is where the antinodes of the sin function appear.
		Now one may ask how the particle gets back and forth in the box if we have nodes in its path where it is not allowed to exist (not even for a fraction of time).
		The wavefunctions of the threedimensional particle in a box is more difficult to visualize since we lack the forth dimension to plot its amplitude.
	itl.chem.ufl.edu /4412_aa/partinbox.html (0 words)

	Particle in a Box
		Since the electrons involved in the transition exhibit similar conditions to those of a particle confined in a one dimensional box, a simple quantum mechanical model can be used to interpret the data.
		In this case, one considers the potential energy of the electron as being constant throughout the length of the molecular box and then rising to infinity at each end of the conjugated portion of the molecule.
		For the particle to be confined within region II, the potential energy outside (regions I and III) is assumed to be infinite.
	bouman.chem.georgetown.edu /S02/lect13/lect13.htm (0 words)

	Particle Soft :: View topic - Particle Links 1.3.0 released
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	forums.particlesoft.net /viewtopic.php?t=215 (0 words)

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	www.pmeasuring.com /particleCounter/air (500 words)

	Main Index - FusionBB Community - Powered by FusionBB
		Particle boxes are boxes of content from your forum.
		We are pleased to announce that as we move forward with the growth of FusionBB, we will be utilizing many of the modifications created by Will (CouchTomatoe).
		We are happy that he has agreed to work with us on many of the tools you will find in version 2.2, like Admin Configurable Navigation Tabs, Admin Configurable Particle Boxes, Post Moderation and many of our Import Scripts.
	www.fusionbb.com (0 words)

	Science Box
		Physicist Observes a Particle and a Wave, Simultaneously
		Scientists observe sound traveling faster than the speed of light.
		Using heat emission observations from the Mars Odyssey spacecraft, researchers were able to map seasonal changes in the temperature of the red planet's surface to locate and measure the buried ice.
	science.box.sk (0 words)

	Jewelry Boxes at Everyday Competitive Prices
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	www.momsjewelrybox.com /Jewelry-Boxes/Jewelry-Boxes-Chests-Index.htm (0 words)

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	www.fusionbb.com /docs/pmwiki.php/Main/CreatingParticleBoxes (543 words)

	Particle in a Box
		At the expense of any pretensions of historical accuracy, I am going to see how many interesting conclusions we can draw from one simple hypothesis posed by Louis Victor Pierre Raymond duc de Broglie in his 26-page doctoral thesis in 1924.
		It had been shown two decades earlier that light, which is certainly a wave, comes quantized in clumps like particles (called photons) with the energy of each photon equal to Planck's constant times its frequency:
		Louis' hypothesis was amazingly simple: he reasoned that if waves are like particles, then maybe particles are like waves.
	musr.physics.ubc.ca /~jess/hr/skept/QM1D/QM1D.html (223 words)

	Motion in a potential
		The motion of the particle is described by the time-dependent Schrödinger equation supplemented with the boundary condition that the wave function at the edge of the rectangular area is zero.
		The wave describing the quantum particle is reflected at the boundaries, a phenomenon analogous to the reflection of light by a mirror.
		The charged quantum particle follows the skipping orbits of the classical particle as long as the whole wave packet is reflected by a single boundary.
	rugth30.phys.rug.nl /quantummechanics/potential.htm (1267 words)

	The particle in a box
		When studying this section, keep in mind that the simplest and earliest system taught, the particle in a box, is still an excellent model (with various adjustments) illuminating the behaviour of electrons in a metal, nucleons in a nucleus, plasma in a star, amongst other systems.
		This is because the particle cannot have infinitely high potential energy behind the walls.
		For a given energy state, a quantum particle may not be anywhere in the box with equal probability.
	psi.phys.wits.ac.za /teaching/Connell/phys284/2005/lecture-02/lecture_02/node9.html (406 words)

	The particle in a box
		When studying this section, keep in mind that the simplest and earliest system taught, the particle in a box, is still an excellent model (with various adjustments) illuminating the behaviour of electrons in a metal, nucleons in a nucleus, plasma in a star, amongst other systems.
		This is because the particle cannot have infinitely high potential energy behind the walls.
		For a given energy state, a quantum particle may not be anywhere in the box with equal probability.
	www.src.wits.ac.za /pages/teaching/Connell/phys284/2005/lecture-02/lecture_02/node9.html (406 words)

	The Particle in a Box / Instructions
		In the case of wavefunctions, the square of the wavefunction at any point is equal to the probability that the particle is at that point: hence the particle is likely to be found at peaks or troughs in the wavefunction, and is never found at the nodes.
		The energy of the particle in the box is partly potential energy, which you might interpret as energy which is not yet ``realized'' as motion but could be.
		Thus the quantum particle is allowed to visit "classically forbidden" regions of the box, i.e.
	www.chem.uci.edu /undergrad/applets/dwell/dwell_explain.htm (3308 words)

	The Particle in a Box / Instructions
		In the case of wavefunctions, the square of the wavefunction at any point is equal to the probability that the particle is at that point: hence the particle is likely to be found at peaks or troughs in the wavefunction, and is never found at the nodes.
		The energy of the particle in the box is partly potential energy, which you might interpret as energy which is not yet ``realized'' as motion but could be.
		Thus the quantum particle is allowed to visit "classically forbidden" regions of the box, i.e.
	www.iperserv.com /formazione/vari/dwell_explain.htm (3318 words)

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