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- 1. Quantum mechanics <ul><li>Quantum mechanics is a branch of physics providing a mathematical description of the wavea particle duality of matter and energy. </li></ul><ul><li>Quantum mechanics are also known as quantum physics or quantum theory. </li></ul><ul><li>Quantum mechanics differs significantly from classical mechanics in its predictions when the scale of observations becomes comparable to the atomic and sub-atomic scale. </li></ul>
- 2. Quantum mechanics <ul><li>The atomic and sub-atomic scale is the so-called quantum realm. </li></ul><ul><li>Phenomena such as superconductivity cannot be explained using classical mechanics. </li></ul><ul><li>The wave ``particle duality'' of energy and matter and the uncertainty principle provide a unified view of the behavior of photons, electrons and other atomic-scale objects in the context of quantum mechanics. </li></ul><ul><li>Many of the results of quantum mechanics do not have models that are easily visualized in terms of classical mechanics ; for instance , the ground state in the quantum mechanical model is a non-zero energy state that is the lowest permitted energy state of a system , rather than a traditional classical system that is thought of as simply being at rest with zero kinetic energy . </li></ul>
- 3. History <ul><li>Each energy element E is proportional to its frequency I: E = h nu where h is Planck's constant. </li></ul><ul><li>Albert Einstein interpreted Planck's quantum hypothesis realistically. </li></ul><ul><li>Albert Einstein used it to explain the photoelectric effect. </li></ul>
- 4. History <ul><li>Developments in quantum mechanics led to its becoming the standard formulation for atomic physics in the mid-1920s. </li></ul><ul><li>The other exemplar that led to quantum mechanics was the study of electromagnetic waves such as light. </li></ul><ul><li>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 be described as a particle - later called the photon - with a discrete quanta of energy that was dependent on its frequency . </li></ul>
- 5. Mathematical formulations <ul><li>Everything appears to have a definite position, a definite momentum, a definite energy, and a definite time of occurrence. </li></ul><ul><li>If one knows the corresponding wave function at the instant before the measurement, one will be able to compute the probability of collapsing into each of the possible eigenstates. </li></ul><ul><li>It is impossible to predict with certainty the result. </li></ul>
- 6. Mathematical formulations <ul><li>One measures the position of the particle. </li></ul><ul><li>Observables can be either continuous or discrete. </li></ul><ul><li>An alternative formulation of quantum mechanics is Feynman's path integral formulation. </li></ul><ul><li>This is the quantum-mechanical counterpart of action principles in classical mechanics. </li></ul>
- 7. Interactions with other scientific theories <ul><li>An important guide for making these choices is the correspondence principle , which states that the predictions of quantum mechanics reduce to those of classical physics when a system moves to higher energies or , equivalently , larger quantum numbers -LRB- i.e. whereas a single particle exhibits a degree of randomness , in systems incorporating millions of particles averaging takes over and , at the high energy limit , the statistical probability of random behavior approaches zero -RRB- . </li></ul><ul><li>Classical mechanics is simply a quantum mechanics of large systems in other words. </li></ul><ul><li>Early attempts to merge quantum mechanics with special relativity involved the replacement of the SchrAdinger equation with a covariant equation such as the Klein-Gordon equation or the Dirac equation. </li></ul>
- 8. Interactions with other scientific theories <ul><li>This ` semi-classical ' approach fails if quantum fluctuations in the electromagnetic field play an important role by charged particles. </li></ul><ul><li>The important role is such as in the emission of photons. </li></ul>
- 9. Quantum mechanics and classical physics <ul><li>Predictions of quantum mechanics have been verified experimentally to an extremely high degree of accuracy. </li></ul><ul><li>* While the seemingly exotic behavior of matter posited by quantum mechanics and relativity theory become more apparent when dealing with extremely fast-moving or extremely tiny particles , the laws of classical Newtonian physics remain accurate in predicting the behavior of the vast majority of large objectsa `` of the order of the size of large molecules and biggera `` at velocities much smaller than the velocity of light . </li></ul>
- 10. Relativity and quantum mechanics <ul><li>He did not accept the more philosophical consequences and interpretations that a single subatomic particle can occupy numerous areas of space at one time. </li></ul><ul><li>He contributed to the field. </li></ul><ul><li>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. </li></ul>
- 11. Relativity and quantum mechanics <ul><li>This effect does not violate causality. </li></ul><ul><li>The two particles can be an arbitrary distance apart. </li></ul><ul><li>No transfer of information happens. </li></ul>
- 12. Philosophical implications <ul><li>Albert Einstein disliked this loss of determinism in measurement. </li></ul><ul><li>Albert Einstein was himself one of the founders of quantum theory. </li></ul><ul><li>Einstein held that there should be a local hidden variable theory underlying quantum mechanics. </li></ul>
- 13. Philosophical implications <ul><li>Einstein held that the present theory was incomplete. </li></ul><ul><li>Experiments have been performed confirming the accuracy of quantum mechanics. </li></ul><ul><li>Experiments demonstrate that the physical world cannot be described by local realistic theories. </li></ul>
- 14. Philosophical implications <ul><li>This is not 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 -LRB- including the observer -RRB- are present in a real physical -LRB- not just formally mathematical , as in other interpretations -RRB- quantum superposition . </li></ul><ul><li>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 did not collapse one would have to bring all these particles back and measure them again , together with the system that was measured originally . </li></ul>
- 15. Applications of quantum mechanics <ul><li>The individual behavior of the subatomic particles that make up all forms of mattera electrons, protons, neutrons, photons and othersa can often only be satisfactorily described using quantum mechanics. </li></ul><ul><li>Recent work on photosynthesis has provided evidence that quantum correlations play an essential role in this most fundamental process of the plant kingdom. </li></ul>
- 16. Free particle <ul><li>For example, consider a free particle. </li></ul><ul><li>This is called an eigenstate of position a generalized position eigenstate. </li></ul>

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