Barack Obama, our next President
"The road ahead will be long. Our climb will be steep," Obama cautioned. Young and charismatic but with little experience on the national level, Obama smashed through racial barriers and easily defeated ...
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#1011467
Oct 25, 2013
The other exemplar that led to quantum mechanics was the study of electromagnetic waves, such as visible and ultraviolet light. When it was found in 1900 by Max Planck that the energy of waves could be described as consisting of small packets or "quanta", Albert Einstein further developed this idea to show that an electromagnetic wave such as light could also be described as a particle (later called the photon) with a discrete quantum of energy that was dependent on its frequency.[7] As a matter of fact, Einstein was able to use the photon theory of light to explain the photoelectric effect, for which he won the Nobel Prize in 1921. This led to a theory of unity between subatomic particles and electromagnetic waves, called wave–particle duality, in which particles and waves were neither one nor the other, but had certain properties of both. Thus coined the term waveparticle duality.
While quantum mechanics traditionally described the world of the very small, it is also needed to explain certain recently investigated macroscopic systems such as superconductors, superfluids, and larger organic molecules.[8] The word quantum derives from the Latin, meaning "how great" or "how much".[9] In quantum mechanics, it refers to a discrete unit that quantum theory assigns to certain physical quantities, such as the energy of an atom at rest (see Figure 1). The discovery that particles are discrete packets of energy with wavelike properties led to the branch of physics dealing with atomic and subatomic systems which is today called quantum mechanics. It is the underlying mathematical framework of many fields of physics and chemistry, including condensed matter physics, solidstate physics, atomic physics, molecular physics, computational physics, computational chemistry, quantum chemistry, particle physics, nuclear chemistry, and nuclear physics.[10] Some fundamental aspects of the theory are still actively studied.[11] 

#1011468
Oct 25, 2013
Its not The deficit that is shrinking... Your brain matter is... 

#1011469
Oct 25, 2013
Quantum mechanics is essential to understanding the behavior of systems at atomic length scales and smaller. If classical mechanics alone governed the workings of an atom, electrons could not really "orbit" the nucleus. Since bodies in circular motion are accelerating, electrons must emit radiation, losing energy and eventually colliding with the nucleus in the process. This clearly contradicts the existence of stable atoms. However, in the natural world, electrons normally remain in an uncertain, nondeterministic, "smeared", probabilistic, wave–particle wavefunction orbital path around (or through) the nucleus, defying the traditional assumptions of classical mechanics and electromagnetism.[12]
Quantum mechanics was initially developed to provide a better explanation and description of the atom, especially the differences in the spectra of light emitted by different isotopes of the same element, as well as subatomic particles. In short, the quantummechanical atomic model has succeeded spectacularly in the realm where classical mechanics and electromagnetism falter. Broadly speaking, quantum mechanics incorporates four classes of phenomena for which classical physics cannot account: 

#1011470
Oct 25, 2013
the brooklyn phaggot was up all night dreaming of my co ck
Quantum mechanics is essential to understanding the behavior of systems at atomic length scales and smaller. If classical mechanics alone governed the workings of an atom, electrons could not really "orbit" the nucleus. Since bodies in circular motion are accelerating, electrons must emit radiation, losing energy and eventually colliding with the nucleus in the process. This clearly contradicts the existence of stable atoms. However, in the natural world, electrons normally remain in an uncertain, nondeterministic, "smeared", probabilistic, wave–particle wavefunction orbital path around (or through) the nucleus, defying the traditional assumptions of classical mechanics and electromagnetism.[12] Quantum mechanics was initially developed to provide a better explanation and description of the atom, especially the differences in the spectra of light emitted by different isotopes of the same element, as well as subatomic particles. In short, the quantummechanical atomic model has succeeded spectacularly in the realm where classical mechanics and electromagnetism falter. Broadly speaking, quantum mechanics incorporates four classes of phenomena for which classical physics cannot account: 

#1011471
Oct 25, 2013
In the mathematically rigorous formulation of quantum mechanics developed by Paul Dirac,[13] David Hilbert,[14] John von Neumann,[15] and Hermann Weyl[16] the possible states of a quantum mechanical system are represented by unit vectors (called "state vectors"). Formally, these reside in a complex separable Hilbert space  variously called the "state space" or the "associated Hilbert space" of the system  that is well defined up to a complex number of norm 1 (the phase factor). In other words, the possible states are points in the projective space of a Hilbert space, usually called the complex projective space. The exact nature of this Hilbert space is dependent on the system  for example, the state space for position and momentum states is the space of squareintegrable functions, while the state space for the spin of a single proton is just the product of two complex planes. Each observable is represented by a maximally Hermitian (precisely: by a selfadjoint) linear operator acting on the state space. Each eigenstate of an observable corresponds to an eigenvector of the operator, and the associated eigenvalue corresponds to the value of the observable in that eigenstate. If the operator's spectrum is discrete, the observable can attain only those discrete eigenvalues.


“Often imitated” Since: Jul 07 28,429 never duplicated 
#1011472
Oct 25, 2013
typical libturd, you can't read. 
#1011473
Oct 25, 2013
In the formalism of quantum mechanics, the state of a system at a given time is described by a complex wave function, also referred to as state vector in a complex vector space.[17] This abstract mathematical object allows for the calculation of probabilities of outcomes of concrete experiments. For example, it allows one to compute the probability of finding an electron in a particular region around the nucleus at a particular time. Contrary to classical mechanics, one can never make simultaneous predictions of conjugate variables, such as position and momentum, with accuracy. For instance, electrons may be considered (to a certain probability) to be located somewhere within a given region of space, but with their exact positions unknown. Contours of constant probability, often referred to as "clouds", may be drawn around the nucleus of an atom to conceptualize where the electron might be located with the most probability. Heisenberg's uncertainty principle quantifies the inability to precisely locate the particle given its conjugate momentum.[18]
According to one interpretation, as the result of a measurement the wave function containing the probability information for a system collapses from a given initial state to a particular eigenstate. The possible results of a measurement are the eigenvalues of the operator representing the observable — which explains the choice of Hermitian operators, for which all the eigenvalues are real. The probability distribution of an observable in a given state can be found by computing the spectral decomposition of the corresponding operator. Heisenberg's uncertainty principle is represented by the statement that the operators corresponding to certain observables do not commute. The probabilistic nature of quantum mechanics thus stems from the act of measurement. This is one of the most difficult aspects of quantum systems to understand. It was the central topic in the famous BohrEinstein debates, in which the two scientists attempted to clarify these fundamental principles by way of thought experiments. In the decades after the formulation of quantum mechanics, the question of what constitutes a "measurement" has been extensively studied. Newer interpretations of quantum mechanics have been formulated that do away with the concept of "wavefunction collapse" (see, for example, the relative state interpretation). The basic idea is that when a quantum system interacts with a measuring apparatus, their respective wavefunctions become entangled, so that the original quantum system ceases to exist as an independent entity. For details, see the article on measurement in quantum mechanics.[19] 

#1011474
Oct 25, 2013
The eyes are useless when your mind is blind with hate old woman... It's the culture... 

#1011475
Oct 25, 2013
You went to a alot of trouble to show us how phrekkin stupid you are... 

#1011476
Oct 25, 2013
LOL 

#1011477
Oct 25, 2013
Generally, quantum mechanics does not assign definite values. Instead, it makes a prediction using a probability distribution; that is, it describes the probability of obtaining the possible outcomes from measuring an observable. Often these results are skewed by many causes, such as dense probability clouds. Probability clouds are approximate, but better than the Bohr model, whereby electron location is given by a probability function, the wave function eigenvalue, such that the probability is the squared modulus of the complex amplitude, or quantum state nuclear attraction.[20][21] Naturally, these probabilities will depend on the quantum state at the "instant" of the measurement. Hence, uncertainty is involved in the value. There are, however, certain states that are associated with a definite value of a particular observable. These are known as eigenstates of the observable ("eigen" can be translated from German as meaning "inherent" or "characteristic").[2 2]
In the everyday world, it is natural and intuitive to think of everything (every observable) as being in an eigenstate. Everything appears to have a definite position, a definite momentum, a definite energy, and a definite time of occurrence. However, quantum mechanics does not pinpoint the exact values of a particle's position and momentum (since they are conjugate pairs) or its energy and time (since they too are conjugate pairs); rather, it provides only a range of probabilities in which that particle might be given its momentum and momentum probability. Therefore, it is helpful to use different words to describe states having uncertain values and states having definite values (eigenstates). Usually, a system will not be in an eigenstate of the observable (particle) we are interested in. However, if one measures the observable, the wavefunction will instantaneously be an eigenstate (or "generalized" eigenstate) of that observable. This process is known as wavefunction collapse, a controversial and muchdebated process[23] that involves expanding the system under study to include the measurement device. If one knows the corresponding wave function at the instant before the measurement, one will be able to compute the probability of the wavefunction collapsing into each of the possible eigenstates. For example, the free particle in the previous example will usually have a wavefunction that is a wave packet centered around some mean position x0 (neither an eigenstate of position nor of momentum). When one measures the position of the particle, it is impossible to predict with certainty the result.[19] It is probable, but not certain, that it will be near x0, where the amplitude of the wave function is large. After the measurement is performed, having obtained some result x, the wave function collapses into a position eigenstate centered at x.[24] 

Since: Jun 13 7,302 
#1011478
Oct 25, 2013
How can you say that? Are you just trying to sound stupid on purpose? The IRS will need thousands more to implement Obamacare and hundreds of navigators are already being paid to teach people how to even sign up for the darn thing. Then there's the government employees who need to speak 150 different languages and too numerous to count government employees to keep up with the too numerous to count regulations to dictate to doctors and insurance companies' the decisions about our health care. What are you talking about? Shrinking the government? Are you just crazy? This administration is hiring government employees to go doortodoor and telephone solicitors to sign more people up for food stamps and welfare. Holy mackerel, Andy. 
“Constitutionalis t” Since: Dec 10 20,806 
#1011479
Oct 25, 2013
The deficit was increased ONE THOUSAND PERCENT after the Democrats took control of all the purse strings of government. The deficit didn't get back down to a relatively constant 1.3 trillion until the TEA Party began to influence the cost of government. Today, the Democrats' version of government has to borrow 1.3 trillion dollars every year just for its daytoday existence. An idiot can tell you that government will collapse. 
“Often imitated” Since: Jul 07 28,429 never duplicated 
#1011480
Oct 25, 2013
you and that pedophile who brags about banging 10 year olds make a cute couple. 
#1011481
Oct 25, 2013
Obamakare is creating a demand for insurance, cancelling existing healthcare policies to justify a demand for obamakare and the exchanges.. It's the culture... 

“Often imitated” Since: Jul 07 28,429 never duplicated 
#1011482
Oct 25, 2013
this is what passes as humor for homer these days. 
#1011483
Oct 25, 2013
Sounds like dem's been watching Star Wars again... 

#1011484
Oct 25, 2013
The time evolution of a quantum state is described by the Schrödinger equation, in which the Hamiltonian (the operator corresponding to the total energy of the system) generates the time evolution. The time evolution of wave functions is deterministic in the sense that  given a wavefunction at an initial time  it makes a definite prediction of what the wavefunction will be at any later time.[25]
During a measurement, on the other hand, the change of the initial wavefunction into another, later wavefunction is not deterministic, it is unpredictable (i.e., random). A timeevolution simulation can be seen here.[26][27] Wave functions change as time progresses. The Schrödinger equation describes how wavefunctions change in time, playing a role similar to Newton's second law in classical mechanics. The Schrödinger equation, applied to the aforementioned example of the free particle, predicts that the center of a wave packet will move through space at a constant velocity (like a classical particle with no forces acting on it). However, the wave packet will also spread out as time progresses, which means that the position becomes more uncertain with time. This also has the effect of turning a position eigenstate (which can be thought of as an infinitely sharp wave packet) into a broadened wave packet that no longer represents a (definite, certain) position eigenstate.[28] 

“Constitutionalis t” Since: Dec 10 20,806 
#1011485
Oct 25, 2013
I'd be impressed if he had any degree at all. I'm betting he couldn't even finish a fine arts degree program. 
#1011486
Oct 25, 2013
dumb carol loves filth and crudeness but only from fellow dumbfk republicans
Some wave functions produce probability distributions that are constant, or independent of time  such as when in a stationary state of constant energy, time vanishes in the absolute square of the wave function. Many systems that are treated dynamically in classical mechanics are described by such "static" wave functions. For example, a single electron in an unexcited atom is pictured classically as a particle moving in a circular trajectory around the atomic nucleus, whereas in quantum mechanics it is described by a static, spherically symmetric wavefunction surrounding the nucleus (Fig. 1)(note, however, that only the lowest angular momentum states, labeled s, are spherically symmetric).[29] The Schrödinger equation acts on the entire probability amplitude, not merely its absolute value. Whereas the absolute value of the probability amplitude encodes information about probabilities, its phase encodes information about the interference between quantum states. This gives rise to the "wavelike" behavior of quantum states. As it turns out, analytic solutions of the Schrödinger equation are available for only a very small number of relatively simple model Hamiltonians, of which the quantum harmonic oscillator, the particle in a box, the hydrogen molecular ion, and the hydrogen atom are the most important representatives. Even the helium atom  which contains just one more electron than does the hydrogen atom  has defied all attempts at a fully analytic treatment. There exist several techniques for generating approximate solutions, however. In the important method known as perturbation theory, one uses the analytic result for a simple quantum mechanical model to generate a result for a more complicated model that is related to the simpler model by (for one example) the addition of a weak potential energy. Another method is the "semiclassical equation of motion" approach, which applies to systems for which quantum mechanics produces only weak (small) deviations from classical behavior. These deviations can then be computed based on the classical motion. This approach is particularly important in the field of quantum chaos. 

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