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Analytical approach to the helium
Analytical approach to the helium

... leads to inaccurate results for the ground-state energy of the helium atom and its isoelectronic sequence. Thus studies of the effects of two-electron correlation have been a subject of interest from the early days of quantum mechanics (Hartree 1957). The ground-state energies of helium and helium-l ...
There is entanglement in the primes
There is entanglement in the primes

... Without trying to be exhaustive, we shall mention some of these attempts that will also aid us to frame the aims of this work (for a review on this topic see [4] and the database [5]). Prime numbers in Physics have been considered as classical or quantum objects. In the first category falls the gas ...
Introduction to Quantum Information
Introduction to Quantum Information

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... Quantum Optics has focused for many years on uncovering what is specifically non-classical about light fields, from the early days of quantum mechanics to current work on quantum information processing. Much of this work has concentrated on the role of discreteness, of the limits of the uncertainty ...
conservation of linear momentum
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... describe the movement of a body; you have also heard about using forces. We will now introduce you to another magnitude that is used to relate the bodie's state of motion with the forces that act on it. We all know that bodies have the capacity of exerting a force on other bodies that are in their w ...
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... Heisenberg’s transition probabilities are well-defined even when there is no value could make a transition. They are like some probabilistic ‘field of force’, existing independently of the presence of a ‘test particle’.7 Third, note also that in this discussion (as well as in Heisenberg’s uncertaint ...
Momentum
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... • When a dish falls, will the impulse be less if it lands on a carpet than if it lands on a hard ceramic tile floor ? • The impulse would be the same for either surface because there is the same momentum change for each. It is the force that is less for the impulse on the carpet because of the great ...
Lecture 5, Conservation Laws, Isospin and Parity
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... Si concentration to 50 p.p.m. and the donor density to 1 × 1014 cm−3, as well as by using techniques to suppress the effects of dipolar interactions among the donors5,12, coherence times of about 10 s have been observed at 1.8 K. This T2 is still two orders of magnitude lower than T1 at this tempera ...
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... 7-69 The wavelengths of the photons emitted by potassium corresponding to transitions from the 4P3/2 and 4P1/2 states to the ground state are 766.41 nm and 769.90 nm. (a) Calculate the energies of these photons in electron volts. (b) The difference in energies of these photons equals the difference ...
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... Complex systems (CS) are frequent in nature. Mathematical methods can be helpful in understanding them. Motivated by the properties of CS we concluded that Fractional order systems are more suitable for describing CS for the following reasons: First they are more natural in describing fractal system ...
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QUANTUM MECHANICS B PHY-413 Note Set No. 7

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The powerpoint presentation of the material

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... Certain properties of physical objects form complementary pairs. The more accurately one property from a pair is known, the less accurately it is possible, in principle, to know the other. The position & momentum of a particle are a complementary pair of properties: ...
AdS/CFT Course Notes - Johns Hopkins University
AdS/CFT Course Notes - Johns Hopkins University

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Renormalization group



In theoretical physics, the renormalization group (RG) refers to a mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales. In particle physics, it reflects the changes in the underlying force laws (codified in a quantum field theory) as the energy scale at which physical processes occur varies, energy/momentum and resolution distance scales being effectively conjugate under the uncertainty principle (cf. Compton wavelength).A change in scale is called a ""scale transformation"". The renormalization group is intimately related to ""scale invariance"" and ""conformal invariance"", symmetries in which a system appears the same at all scales (so-called self-similarity). (However, note that scale transformations are included in conformal transformations, in general: the latter including additional symmetry generators associated with special conformal transformations.)As the scale varies, it is as if one is changing the magnifying power of a notional microscope viewing the system. In so-called renormalizable theories, the system at one scale will generally be seen to consist of self-similar copies of itself when viewed at a smaller scale, with different parameters describing the components of the system. The components, or fundamental variables, may relate to atoms, elementary particles, atomic spins, etc. The parameters of the theory typically describe the interactions of the components. These may be variable ""couplings"" which measure the strength of various forces, or mass parameters themselves. The components themselves may appear to be composed of more of the self-same components as one goes to shorter distances.For example, in quantum electrodynamics (QED), an electron appears to be composed of electrons, positrons (anti-electrons) and photons, as one views it at higher resolution, at very short distances. The electron at such short distances has a slightly different electric charge than does the ""dressed electron"" seen at large distances, and this change, or ""running,"" in the value of the electric charge is determined by the renormalization group equation.
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