Basic Theoretical Physics: A Concise Overview P37 pot

... Physics (Statistical Operator; Trace Formalism) In addition there is a Hermitian density operator ˆ, also called state oper- ator or statistical operator, whose eigenvalues are just the probabilities ... of avoid- ing diagonalizing the Hamiltonian there is the penalty of more complicated calculations 2 . For example, it is easy to calculate the partition function if one has already diagona...

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... 331 equations 163 mean field approximation (bi-linearized) of a Hamiltonian 334 mean field approximations 405, 408 measurable quantities (“observables”) in quantum mechanics 215 measurable quantities ... 402 main-sequence stars 388 MAPLE, MATHEMATICA 161 Markoff chain 412 mass defect 104 mathematical (versus physical) pendulum 75 Maxwell ’s displacement current 153, 156 ’s equations in Gaussia...

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... linear momentum for a planetary system. The additional conser- vation law only applies for potentials of the form A/ r (as well as A · r potentials), corresponding to the fact that for these potentials ... not just a universal number, but proportional to the mass M of the respective central star.) As already mentioned, Kepler’s second law is also known as the law of equal areas and is eq...

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... 50 8 Lagrange Formalism I: Lagrangian and Hamiltonian Compared to the Newtonian equations of motion, the Lagrangian formal- ism thus: a) not only has the decisive advantage of optimum ... center-of-mass coordinates and the azimuthal angle ϕ are therefore cyclic; thus one has the total linear momentum and the orbital angular mo- mentum as conserved quantities, and because the Lagrangian ... U...

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... inertial frames must be made via a Lorentz transforma- tion not a Galilean transformation. As a consequence, as already mentioned 6 , with these new insights into space and time Newtonian mechanics, ... bracket [A, B] P of two measurable quantities A and B is intimately related to the so-called commutator of the quantum mechanical operators ˆ A and ˆ B, i.e., [A, B] P → i   ˆ A...

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... resonance phenomena using mathematical computer tools such as MAPLE or MATHEMATICA. See for example [12] as a rec- ommendable presentation.) 20.3 Planar Electromagnetic Waves; Spherical Waves ... (20.4) The scalar potential φ(r,t) and vector potential A( r,t)mustnowbe calculated simultaneously. However, they are not unique but can be “gauged” (i.e., changed according to a gauge transform...

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... (i.e., also S ∼ k), i.e., one is dealing with totally usual relations as in a vacuum (the so-called ordinary beam). In contrast, for orthogonal polarization the vectors E and D (and S and k) have ... that one speaks of an extraordinary beam. If the phase-propagation vector k is, e.g., in the (x 1 ,x 3 )-plane under a gen- eral angle, then the in-plane polarized wave is ordinary,whereasthe...

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... temperature T decreases gradually, and as a consequence, as we see from the above series of equations, the radius of the star and its luminosity increase, whereas the total mass remains approximately ... numbers must be regarded as only very approximate, especially with regard to black holes. The point is, however, that the gravitational attraction can be counter- acted by the degeneracy pr...

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... the high-temperature behavior can be calculated exactly and analytically, c) and in-between a reasonable interpolation is given. The Debye approximation extrapolates the ω 2 -behavior from low ... ) is based on the fact that in a snapshot of the momentary spin configuration spins at two different places, if their separation |r −r  | is much smaller than ξ(T ), are almost always parallel, ....

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... as the conjugate Lagrange parameter regulating fluctua- tions in V . These Legendre transformations are mathematically analogous to the transition from the Lagrange function L(v, ) 2 to the Hamilton ... 55 and reaction . . . 8, 38, 119 activated state (thermodynamics, k B T  E i ) 341 active charge 119 active gravitational mass 8 actual (versus virtual) orbits 47, 48 addition rules for angula...

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