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What are the benefits of quantum mechanics over classical mechanics?
Wiki User
∙ 14y ago
Well, that depends on what you meant by "benefits". Either way, both of them have their limitations. Classical mechanics can not be used to accurately describe an atom. Just as quantum mechanics would be useless if you were asked to find the terminal velocity of a Baseball. Both areas have give us a plethora of inventions and technologies that would not have existed otherwise. Now in terms of learning the topics, quantum mechanics is deemed by some to be more interesting because of its mystery (probabilistic predictions) versus classical mechanic's seemingly dry Hamiltonians and Lagranians. Both topics are very powerful tools that are used to solve complicated problems, and one is not really better than the other but I believe that neither is complete. I hope that helped.
Wiki User
∙ 14y ago
Wiki User
∙ 12y agoA few main differences:
1) Classical mechanics assumes that certain physical quantities -- such as charge or light energy or angular momentum -- can be reduced to an infinitely small level. For example, CM assumes that there is no level of angular momentum below which a particle can not go.
QM, on the other hand, states that there ARE certain levels of these quantities, below which they can not go. There can be no amount of charge smaller than the electron charge. The energy of light at a certain frequency can not be smaller than the product of that frequency and Planck's Constant ('h'). And a particle can not have less angular momentum than h over 2pi. There are innumerable other examples of quantized physical quantitites.
2) CM assumes that, IN THEORY at least, one can predict the final result of an interaction knowing enough of the initial conditions with enough precision. For instance, if one knows the initial speed and direction of a kicked football, as well as the atmospheric conditions, one could calculate the exact place where it will land. Similarly, CM assumes that one could know where an electron will land on a detector once it has left the electron gun and goes through one of two slits.
QM assumes that it is not possible to do this for small particles EVEN IN THEORY. In contrast, QM states that one can only describe the PROBABILITY of a small object ending up at a certain place. It is NOT the case, says QM, that we lack cleverness or good enough instruments -- it is that lack of precision is an inherent fact of our Universe.
3) CM assumes as "obvious" that, if an object goes from one state (say, an electron orbit of one Bohr radius ('Rb') from the nucleus) to another (say, an electron orbit of distance 2Rb from the nucleus), that object MUST have, for some period of times, been part way between those two states.
QM states that this transition occurs instantaneously, with that object spending zero time part way between these two states. In the example above, an electron can go from an orbit at distance Rb from the nucleus to an orbit at a distance 2Rb from the nucleus, without EVER having been at a distance of 1.5 Rb from the nucleus.
Werner Heisenberg once quipped (something like), "If you aren't bothered by the implications of quantum mechanics, then you don't understand it."
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Why was quantum mechanics invented?
Quantum Mechanics is one of the three branches of Modern Physics, being the other two, Classical Mechanics and Relativist Mechanics. Quantum Mechanics is needed to learn the intimate behavior of the smallest particles existent: subatomic particles. It deals with the interaction amongst, the forms of energy they receive and deliver, and the way they emit energy, a way done in packets, or quanta, also called photons. Quantum Mechanics is one of the base knowledges for the design of modern electronics.
Merits of quantum theory over classical theory?
Unlike other physical theories, quantum mechanics was the invention of not only one or two scientists. Planck, Einstein, Bohr, Heisenberg, Born, Jordan, Pauli, Fermi, Schrodinger, Dirac, de Broglie, Bose are the scientists that made notable contributions to the invention of quantum theory. The axioms of quantum mechanics provide a consistent framework in which it is once again possible to predict the results of experiment, at least statistically.Its fundamental features are that a property does not exist unless it is measured, and that indeterminacy is a fundamental property of the universe. The main merit of QM is that its predictions -- such as that for the two slit experiment -- perfectly match the results, while classical mechanics fails to do so. For a scientist, nothing else much matters.
What is the Difference between relativity and quantum mechanics?
Quantum Mechanics is the study of the intimate behavior of the smallest forms of particles, and their interaction amongst, with special emphasys on the emissions of energy, which is delivered in quanta, or photons. Wave Mechanics is the study of many physical phenomena that happen in a non linear and recurrent behavior, usually addressed as wave, with special emphasys in both the features of said wave, and the energy that involves specific wave phenomena.
Why you use some classical mechanics in quantum mechanics?
That has been a topic of much debate since th1900's. There has been no fully successful tying of the two branches of physics yet but, many proposed theories have made great leaps forward to the answer. For example quantum gravity theory and the string theory, the latter being the more current and relevant.There are two areas in which the transition from quantum mechanics to classical mechanics is rather obvious: Statistical thermodynamics and wave-particle duality.Answer2:Classical and Quantum Mechanics merge in Quaternion Mechanics.Quaternion Mechanics consists of Quaternion quantities like energyW = -vh/r + cP where -vh/r is the scalar enrgy and cP=cmV is the vector energy.Classical and Quantum Mechanics need Quaternion quantities. In general the potential energy -vh/r is a scalar aka a Boson and vector energy cP is a vector aka a Fermion. Bosons/Scalars have integer spin and Fermions/Vectors have 1/2 integer spin.For the most part like Newtonian Physics use only scalars -mGM/r a scalar and no vectors. Likewise, Quantum mechanics use mostly Fermions or Vectors and few scalars. The speed of light is a scalar as is Planck's Constant h.Quaternion Mechanics merges Classical and Quantum Physics.The Laws of Quaternion Mechanics are:0 = XB = [d/dr, DEL] [B,B] = [dB/dr -DEL.B, dB/dr + DEL B ]0 = X2B = [(d2/dr2 - DEL2), 2d/dr DEL] [-vh/r,cP]This Quaternion Wave gives thescalar/Boson wave -(d2/dr2 - DEL2)vh/r - 2d/dr DEL.cP =0and thevector/Fermion particle (d2/dr2 - DEL2)cP + 2d/dr DEL -vh/r =0In Nature, Quaternions rule and Quaternions combine Bosons and Fermions.A Quaternion can be a Boson or a Fermion or Both as inX2W =[ -(d2/dr2 - DEL2)vh/r - 2d/dr DEL.cP,(d2/dr2 - DEL2)cP + 2d/dr( DEL -vh/r + DELxcP) ]Quaternions consist of Scalars and Vectors , Bosons and Fermions.
Why don't i understand quantum theory?
Quantum Mechanics is inherently difficult to understand. In fact the well known physicist Richard Feynman, an expert on Quantum Mechanics, said: "It is safe to say that nobody understands Quantum Mechanics."
Why was quantum mechanics invented?
Quantum Mechanics is one of the three branches of Modern Physics, being the other two, Classical Mechanics and Relativist Mechanics. Quantum Mechanics is needed to learn the intimate behavior of the smallest particles existent: subatomic particles. It deals with the interaction amongst, the forms of energy they receive and deliver, and the way they emit energy, a way done in packets, or quanta, also called photons. Quantum Mechanics is one of the base knowledges for the design of modern electronics.
Merits of quantum theory over classical theory?
Unlike other physical theories, quantum mechanics was the invention of not only one or two scientists. Planck, Einstein, Bohr, Heisenberg, Born, Jordan, Pauli, Fermi, Schrodinger, Dirac, de Broglie, Bose are the scientists that made notable contributions to the invention of quantum theory. The axioms of quantum mechanics provide a consistent framework in which it is once again possible to predict the results of experiment, at least statistically.Its fundamental features are that a property does not exist unless it is measured, and that indeterminacy is a fundamental property of the universe. The main merit of QM is that its predictions -- such as that for the two slit experiment -- perfectly match the results, while classical mechanics fails to do so. For a scientist, nothing else much matters.
What is the Difference between relativity and quantum mechanics?
Quantum Mechanics is the study of the intimate behavior of the smallest forms of particles, and their interaction amongst, with special emphasys on the emissions of energy, which is delivered in quanta, or photons. Wave Mechanics is the study of many physical phenomena that happen in a non linear and recurrent behavior, usually addressed as wave, with special emphasys in both the features of said wave, and the energy that involves specific wave phenomena.
Why you use some classical mechanics in quantum mechanics?
That has been a topic of much debate since th1900's. There has been no fully successful tying of the two branches of physics yet but, many proposed theories have made great leaps forward to the answer. For example quantum gravity theory and the string theory, the latter being the more current and relevant.There are two areas in which the transition from quantum mechanics to classical mechanics is rather obvious: Statistical thermodynamics and wave-particle duality.Answer2:Classical and Quantum Mechanics merge in Quaternion Mechanics.Quaternion Mechanics consists of Quaternion quantities like energyW = -vh/r + cP where -vh/r is the scalar enrgy and cP=cmV is the vector energy.Classical and Quantum Mechanics need Quaternion quantities. In general the potential energy -vh/r is a scalar aka a Boson and vector energy cP is a vector aka a Fermion. Bosons/Scalars have integer spin and Fermions/Vectors have 1/2 integer spin.For the most part like Newtonian Physics use only scalars -mGM/r a scalar and no vectors. Likewise, Quantum mechanics use mostly Fermions or Vectors and few scalars. The speed of light is a scalar as is Planck's Constant h.Quaternion Mechanics merges Classical and Quantum Physics.The Laws of Quaternion Mechanics are:0 = XB = [d/dr, DEL] [B,B] = [dB/dr -DEL.B, dB/dr + DEL B ]0 = X2B = [(d2/dr2 - DEL2), 2d/dr DEL] [-vh/r,cP]This Quaternion Wave gives thescalar/Boson wave -(d2/dr2 - DEL2)vh/r - 2d/dr DEL.cP =0and thevector/Fermion particle (d2/dr2 - DEL2)cP + 2d/dr DEL -vh/r =0In Nature, Quaternions rule and Quaternions combine Bosons and Fermions.A Quaternion can be a Boson or a Fermion or Both as inX2W =[ -(d2/dr2 - DEL2)vh/r - 2d/dr DEL.cP,(d2/dr2 - DEL2)cP + 2d/dr( DEL -vh/r + DELxcP) ]Quaternions consist of Scalars and Vectors , Bosons and Fermions.
Why has the model of the atom changed over time?
Improved knowledge of the atom via new experiments and development of new theories (e.g. quantum mechanics).
Is quantum mechanics for real?
Your question is on the order of asking, "Does the Earth go around the Sun?" Every experiment done over the last eighty years or so has confirmed the accuracy of quantum mechanics -- in one case, the agreement between theory and experiment was within ten parts per BILLION. I'm fully aware that QM doesn't agree with what we "know" about our world. Neils Bohr, one of the founders of QM, has been quoted as saying, "Anyone who is not shocked by quantum theory has not understood it." Nevertheless, QM is as true as a helio-centric solar system.
Why don't i understand quantum theory?
Quantum Mechanics is inherently difficult to understand. In fact the well known physicist Richard Feynman, an expert on Quantum Mechanics, said: "It is safe to say that nobody understands Quantum Mechanics."
What is quantum Internet?
Quantum internet refers to the application of quantum cryptography over a "quantum" network. Quantum cryptography yields unbreakable encryption due to the uncertainty principle. The technology is still very new and needs more research for commercialization.
How would you know the hypothesis for growing plants?
this: 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. 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 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. During a measurement, on the other hand, the change of the wavefunction into another one is not deterministic, but rather unpredictable, i.e., random. A time-evolution simulation can be seen here. Wave functions can change as time progresses. An equation known as the Schrödinger equation describes how wave functions change in time, 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. This also has the effect of turning position eigenstates (which can be thought of as infinitely sharp wave packets) into broadened wave packets that are no longer position eigenstates. Some wave functions produce probability distributions that are constant, or independent of time, such as when in a stationary state of constant energy, time drops out of 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. 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 wave-like behavior of quantum states. It turns out that analytic solutions of Schrödinger's equation are only available for a small number of 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 hydrogen, defies all attempts at a fully analytic treatment. There exist several techniques for generating approximate solutions. For instance, in the method known as perturbation theory one uses the analytic results for a simple quantum mechanical model to generate results for a more complicated model related to the simple model by, for example, the addition of a weak potential energy. Another method is the "semi-classical equation of motion" approach, which applies to systems for which quantum mechanics produces weak deviations from classical behavior. The deviations can be calculated based on the classical motion. This approach is important for the field of quantum chaos. There are numerous mathematically equivalent formulations of quantum mechanics. One of the oldest and most commonly used formulations is the transformation theory proposed by Cambridge theoretical physicist Paul Dirac, which unifies and generalizes the two earliest formulations of quantum mechanics, matrix mechanics (invented by Werner Heisenberg) and wave mechanics (invented by Erwin Schrödinger).In this formulation, the instantaneous state of a quantum system encodes the probabilities of its measurable properties, or "observables". Examples of observables include energy, position, momentum, and angular momentum. Observables can be either continuous (e.g., the position of a particle) or discrete (e.g., the energy of an electron bound to a hydrogen atom). An alternative formulation of quantum mechanics is Feynman's path integral formulation, in which a quantum-mechanical amplitude is considered as a sum over histories between initial and final states; this is the quantum-mechanical counterpart of action principles in classical mechanics. cheers!
Where do mechanics live?
all over the world
what is the E8?
experiment safely, swiftly and calmly over and again until you know that you know that quantum physics in all its many forms is true; but do not forget the classical physics of the past. What do we get when the past and present meet? Hmm...???
Who was Niels Bohr and was did he do?
One of the physicists that worked on Quantum Mechanics in the 1920s and 1930s. He is Danish and lived in Copenhagen. He is most popularly known for his interpretation of Quantum Mechanics that came to be called the Copenhagen Interpretation (which Einstein strongly opposed).During WW2 following the Nazi invasion of Denmark, he nearly died in a unpressurized part of a British bomber from lack of oxygen, even though he was given an oxygen mask and bottle, when the mask came loose from his large head and he blacked out before he could put it back.
