Basic Theoretical Physics: A Concise Overview P6 pot
Basic Theoretical Physics: A Concise Overview P6 pot
... 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...
Basic Theoretical Physics: A Concise Overview P43 potx
... 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...
Basic Theoretical Physics: A Concise Overview P5 potx
... 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...
Basic Theoretical Physics: A Concise Overview P7 pot
... 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...
Basic Theoretical Physics: A Concise Overview P17 potx
... 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...
Basic Theoretical Physics: A Concise Overview P20 potx
... (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...
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...
Basic Theoretical Physics: A Concise Overview P38 potx
... 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...
Basic Theoretical Physics: A Concise Overview P39 pot
... 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, ....
Basic Theoretical Physics: A Concise Overview P42 potx
... 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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