Everything about Quantum Mechanics totally explained
Quantum mechanics is the study of
mechanical systems whose dimensions are close to or below the
atomic scale, such as
molecules,
atoms,
electrons,
protons and other
subatomic particles. Quantum mechanics is a fundamental branch of
physics with wide applications. Quantum theory generalizes
classical mechanics and provides
accurate descriptions for many previously unexplained
phenomena such as
black body radiation and stable
electron orbits. The effects of quantum mechanics are typically not observable on
macroscopic scales, but become evident at the
atomic and
subatomic level. There are however exceptions to this rule such as
superfluidity.
Overview
The word “quantum” came from the Latin word which means "what quantity". 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, at right). The discovery that
waves have discrete energy packets (called
quanta) that behave in a manner similar to
particles led to the branch of physics that deals with atomic and subatomic systems which we today call quantum mechanics. It is the underlying
mathematical framework of many fields of
physics and
chemistry, including
condensed matter physics,
solid-state physics,
atomic physics,
molecular physics,
computational chemistry,
quantum chemistry,
particle physics, and
nuclear physics. The foundations of quantum mechanics were established during the first half of the twentieth century by
Werner Heisenberg,
Max Planck,
Louis de Broglie,
Albert Einstein,
Niels Bohr,
Erwin Schrödinger,
Max Born,
John von Neumann,
Paul Dirac,
Wolfgang Pauli and
others. Some fundamental aspects of the theory are still actively studied.
Quantum mechanics is essential to understand the behavior of systems at
atomic length scales and smaller. For example, if
Newtonian mechanics governed the workings of an atom,
electrons would rapidly travel towards and collide with the
nucleus, making stable atoms impossible. However, in the natural world the electrons normally remain in an unknown orbital path around the nucleus, defying classical electromagnetism.
Quantum mechanics was initially developed to provide a better explanation of the atom, especially the
spectra of
light emitted by different
atomic species. The quantum theory of the atom was developed as an explanation for the electron's staying in its
orbital, which couldn't be explained by Newton's laws of motion and by
Maxwell's laws of classical electromagnetism.
In the formalism of quantum mechanics, the state of a system at a given time is described by a
complex wave function (sometimes referred to as orbitals in the case of atomic electrons), and more generally, elements of a complex
vector space. 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 arbitrary accuracy. For instance, electrons may be considered to be located somewhere within a region of space, but with their exact positions being 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. It should be stressed that the electron itself isn't spread out over such cloud regions. It is either in a particular region of space, or it isn't [citationneeded]. Heisenberg's
uncertainty principle quantifies the inability to precisely locate the particle.
The other
exemplar that led to quantum mechanics was the study of
electromagnetic waves such as 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 exploited this idea to show that an electromagnetic wave such as light could be described by a particle called the
photon with a discrete energy dependent on its frequency. 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. While quantum mechanics describes the world of the very small, it also is needed to explain certain “
macroscopic quantum systems” such as
superconductors and
superfluids.
Broadly speaking, quantum mechanics incorporates four classes of phenomena that classical physics can't account for: (i) the
quantization (discretization) of
certain physical quantities, (ii)
wave-particle duality, (iii) the
uncertainty principle, and (iv)
quantum entanglement. Each of these phenomena is described in detail in subsequent sections.
History
The
history of quantum mechanics began essentially with the 1838 discovery of
cathode rays by
Michael Faraday, the 1859 statement of the
black body radiation problem by
Gustav Kirchhoff, the 1877 suggestion by
Ludwig Boltzmann that the energy states of a physical system could be discrete, and the 1900 quantum hypothesis by
Max Planck that any energy is radiated and absorbed in quantities divisible by discrete ‘energy elements’, E, such that each of these energy elements is proportional to the
frequency ν with which they each individually radiate
energy, as defined by the following formula:
»
where
h is
Planck's Action Constant. Although Planck insisted that this was simply an aspect of the absorption and radiation of energy and had nothing to do with the physical reality of the energy itself, in 1905, to explain the
photoelectric effect (1839), for example that shining light on certain materials can function to eject electrons from the material,
Albert Einstein postulated, as based on Planck’s quantum hypothesis, that
light itself consists of individual quanta, which later came to be called
photons (1926).
From Einstein's simple postulation was borne a flurry of debating, theorizing and testing, and thus, the entire field of
quantum physics.
Relativity and quantum mechanics
The modern world of physics is notably founded on two tested and demonstrably sound theories of general relativity and quantum mechanics —theories which appear to contradict one another.
The defining postulates of both Einstein's theory of relativity and quantum theory are indisputably supported by rigorous and repeated empirical evidence. However, while they don't directly contradict each other theoretically (at least with regard to primary claims), they're resistant to being incorporated within one cohesive model.
Einstein himself is well known for rejecting some of the claims of quantum mechanics.
While clearly inventive in this field, he didn't accept the more philosophical consequences and interpretations of quantum mechanics, such as the lack of deterministic
causality and the assertion that a single subatomic particle can occupy numerous areas of space at one time. He also was the first to notice some of the apparently exotic consequences of
entanglement and used them to formulate the
Einstein-Podolsky-Rosen paradox, in the hope of showing that quantum mechanics has unacceptable implications. This was 1935, but in 1964 it was shown by John Bell (see
Bell inequality) that Einstein's assumption that quantum mechanics is correct, but has to be completed by
hidden variables, was based on wrong philosophical assumptions: according to the paper of J. Bell and the
Copenhagen interpretation (the common interpretation of quantum mechanics by physicists for decades), and contrary to Einstein's ideas, quantum mechanics is
- neither a "realistic" theory (since quantum measurements don't state pre-existing properties, but rather they prepare properties)
nor a local theory (essentially not, because the state vector determines simultaneously the probability amplitudes at all sites, ).
The Einstein-Podolsky-Rosen paradox shows in any case that there exist experiments by which one can measure the state of one particle and instantaneously change the state of its entangled partner, although the two particles can be an arbitrary distance apart; however, this effect doesn't violate causality, since no transfer of information happens. These experiments are the basis of some of the most topical applications of the theory, quantum cryptography, which works well, although at small distances of typically
Consider x = 0
sin 0 = 0, cos 0 = 1. To satisfy D = 0 (cos term is removed)
Now Consider:
at X = L,
If C = 0 then for all x and would conflict with Born interpretation
therefore sin kL must be satisfied by » :
In this situation, n must be an integer showing the quantization of the energy levels.
Applications
Quantum mechanics has had enormous success in explaining many of the features of our world. The individual behaviour of the subatomic particles that make up all forms of matter—electrons, protons, neutrons, photons and others—can often only be satisfactorily described using quantum mechanics. Quantum mechanics has strongly influenced string theory, a candidate for a theory of everything (see reductionism). It is also related to statistical mechanics.
Quantum mechanics is important for understanding how individual atoms combine covalently to form chemicals or molecules. The application of quantum mechanics to chemistry is known as quantum chemistry. (Relativistic) quantum mechanics can in principle mathematically describe most of chemistry. Quantum mechanics can provide quantitative insight into ionic and covalent bonding processes by explicitly showing which molecules are energetically favorable to which others, and by approximately how much. Most of the calculations performed in computational chemistry rely on quantum mechanics.
Much of modern technology operates at a scale where quantum effects are significant. Examples include the laser, the transistor, the electron microscope, and magnetic resonance imaging. The study of semiconductors led to the invention of the diode and the transistor, which are indispensable for modern electronics.
Researchers are currently seeking robust methods of directly manipulating quantum states. Efforts are being made to develop quantum cryptography, which will allow guaranteed secure transmission of information. A more distant goal is the development of quantum computers, which are expected to perform certain computational tasks exponentially faster than classical computers. Another active research topic is quantum teleportation, which deals with techniques to transmit quantum states over arbitrary distances.
In many devices, even the simple light switch, quantum tunneling is vital, as otherwise the electrons in the electric current couldn't penetrate the potential barrier made up, in the case of the light switch, of a layer of oxide. Flash memory chips found in USB drives also use quantum tunneling to erase their memory cells.
Philosophical consequences
» :Main article: Interpretation of quantum mechanics
Since its inception, the many counter-intuitive results of quantum mechanics have provoked strong philosophical debate and many interpretations. Even fundamental issues such as Max Born's basic rules concerning probability amplitudes and probability distributions took decades to be appreciated.
The Copenhagen interpretation, due largely to the Danish theoretical physicist Niels Bohr, is the interpretation of quantum mechanics most widely accepted amongst physicists. According to it, the probabilistic nature of quantum mechanics predictions can't be explained in terms of some other deterministic theory, and doesn't simply reflect our limited knowledge. Quantum mechanics provides probabilistic results because the physical universe is itself probabilistic rather than deterministic.
Albert Einstein, himself one of the founders of quantum theory, disliked this loss of determinism in measurement. (Hence his famous quote "God doesn't play dice with the universe.") He held that there should be a local hidden variable theory underlying quantum mechanics and consequently the present theory was incomplete. He produced a series of objections to the theory, the most famous of which has become known as the EPR paradox. John Bell showed that the EPR paradox led to experimentally testable differences between quantum mechanics and local theories. Experiments have been taken as confirming that quantum mechanics is correct and the real world must be described in terms of nonlocal theories.
The writer C. S. Lewis viewed quantum mechanics as incomplete, because notions of indeterminism didn't agree with his
religious beliefs. Lewis, a professor of English, was of the opinion that the Heisenberg uncertainty principle was more of an epistemic limitation than an indication of ontological indeterminacy, and in this respect believed similarly to many advocates of hidden variables theories. The Bohr-Einstein debates provide a vibrant critique of the Copenhagen Interpretation from an epistemological point of view.
The Everett many-worlds interpretation, formulated in 1956, holds that all the possibilities described by quantum theory simultaneously occur in a "multiverse" composed of mostly independent parallel universes. This isn't accomplished by introducing some new axiom to quantum mechanics, but on the contrary by removing the axiom of the collapse of the wave packet: All the possible consistent states of the measured system and the measuring apparatus (including the observer) are present in a real physical (not just formally mathematical, as in other interpretations) quantum superposition. (Such a superposition of consistent state combinations of different systems is called an entangled state.) While the multiverse is deterministic, we perceive non-deterministic behavior governed by probabilities, because we can observe only the universe, for example the consistent state contribution to the mentioned superposition, we inhabit. Everett's interpretation is perfectly consistent with John Bell's experiments and makes them intuitively understandable. However, according to the theory of quantum decoherence, the parallel universes will never be accessible for us, making them physically meaningless. This inaccessibility can be understood as follows: once a measurement is done, the measured system becomes entangled with both the physicist who measured it and a huge number of other particles, some of which are photons flying away towards the other end of the universe; in order to prove that the wave function didn't collapse one would have to bring all these particles back and measure them again, together with the system that was measured originally. This is completely impractical, but even if one can theoretically do this, it would destroy any evidence that the original measurement took place (including the physicist's memory).
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