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... Lorentz force from the others magnetic field. For more information, see the article Ampres force law. ...
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Chapter 15 Solutions

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... Abstract In preceding chapters we have used a master-equation treatment to calculate the photon statistics inside an optical cavity when the internal field is damped. This approach is based on treating the field external to the cavity, to which the system is coupled, as a heat bath. The heat bath is ...
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... solved exactly for its bound states (energy spectrum and wave functions) [23,24]. So, it is natural that the relativistic effects for a charged particle under the action of this potential could become important, especially for a strong coupling. Within this annals, we have also studied the exact ana ...
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The Quantum Vacuum and the Cosmological Constant Problem

... As a suggestion towards a solution to the huge vacuum energy density problem, Bohr contemplates compensation mechanisms between positive and negative zeropoint field energies but remarks that ‘[a]t present, it would seem futile to pursue such considerations more closely...’. In his historical surve ...
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... exactly), make your best guess for the ground state wavefunction ΨGS ,Guess ( r ) (make sure it is normalized: ΨGS ,Guess ΨGS ,Guess = 1 ) and calculate the expectation value of the Hamiltonian with this wavefunction: ΨGS ,Guess Η ΨGS ,Guess . The true ground state energy is guaranteed to be less th ...
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... material of dielectric constant κ is inserted a distance x into the capacitor, as shown in Figure P26.56. Assume that d is much smaller than x. (a) Find the equivalent capacitance of the device. (b) Calculate the energy stored in the capacitor, letting ΔV represent the potential difference. (c) Find ...
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Aalborg Universitet BASES OF CREATIVE PARTICLES OF HIGGS THEORY (CPH THEORY)

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Casimir effect



In quantum field theory, the Casimir effect and the Casimir–Polder force are physical forces arising from a quantized field. They are named after the Dutch physicist Hendrik Casimir.The typical example is of two uncharged metallic plates in a vacuum, placed a few nanometers apart. In a classical description, the lack of an external field means that there is no field between the plates, and no force would be measured between them. When this field is instead studied using the QED vacuum of quantum electrodynamics, it is seen that the plates do affect the virtual photons which constitute the field, and generate a net force—either an attraction or a repulsion depending on the specific arrangement of the two plates. Although the Casimir effect can be expressed in terms of virtual particles interacting with the objects, it is best described and more easily calculated in terms of the zero-point energy of a quantized field in the intervening space between the objects. This force has been measured and is a striking example of an effect captured formally by second quantization. However, the treatment of boundary conditions in these calculations has led to some controversy.In fact, ""Casimir's original goal was to compute the van der Waals force between polarizable molecules"" of the metallic plates. Thus it can be interpreted without any reference to the zero-point energy (vacuum energy) of quantum fields.Dutch physicists Hendrik B. G. Casimir and Dirk Polder at Philips Research Labs proposed the existence of a force between two polarizable atoms and between such an atom and a conducting plate in 1947, and, after a conversation with Niels Bohr who suggested it had something to do with zero-point energy, Casimir alone formulated the theory predicting a force between neutral conducting plates in 1948; the former is called the Casimir–Polder force while the latter is the Casimir effect in the narrow sense. Predictions of the force were later extended to finite-conductivity metals and dielectrics by Lifshitz and his students, and recent calculations have considered more general geometries. It was not until 1997, however, that a direct experiment, by S. Lamoreaux, described above, quantitatively measured the force (to within 15% of the value predicted by the theory), although previous work [e.g. van Blockland and Overbeek (1978)] had observed the force qualitatively, and indirect validation of the predicted Casimir energy had been made by measuring the thickness of liquid helium films by Sabisky and Anderson in 1972. Subsequent experiments approach an accuracy of a few percent.Because the strength of the force falls off rapidly with distance, it is measurable only when the distance between the objects is extremely small. On a submicron scale, this force becomes so strong that it becomes the dominant force between uncharged conductors. In fact, at separations of 10 nm—about 100 times the typical size of an atom—the Casimir effect produces the equivalent of about 1 atmosphere of pressure (the precise value depending on surface geometry and other factors).In modern theoretical physics, the Casimir effect plays an important role in the chiral bag model of the nucleon; in applied physics, it is significant in some aspects of emerging microtechnologies and nanotechnologies.Any medium supporting oscillations has an analogue of the Casimir effect. For example, beads on a string as well as plates submerged in noisy water or gas illustrate the Casimir force.
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