... (26.1)
The harmonic oscillator is important inter alia because a potential energy
V (x) in the vicinity of a local minimum can almost always be approximated
by a parabola (which is the characteristic ... that V (r) should be rota-
tionally invariant.
Next, the usual ansatz for stationary states is made:
ψ(r,t)=u(r) · e
−iEt/
.
Then, in spherical coordinates a product ansatz (separati...
... r and m
s
refer to the planet, and R and M
s
to the central star (“sun”),
while γ is the gravitational constant. Here the [gravitational] masses play
the role of gravitational charges, similar ... “active” and
“passive” gravitational masses are equal (see the end of the preceding sec-
tion), i.e., on the one hand, a body with an (active) gravitational charge M
s
generates a gravitational...
... 11.3.
TheimportanceoftheEuler angles goes far beyond theoretical mechanics
as demonstrated by the technical importance of the Cardani suspension.
Fig. 11.3. The figure illustrates a so-called Cardani sus-
pension, ... axis the ω-lines are hyperbolas,
∝
ε
α
ω
2
α
− ε
γ
ω
2
γ
,
i.e., along one diagonal axis they are attracted, but along the other diagonal
axis there is repulsion, and the...
... of
q
1
q
2
, whereas the gravitational force is always attractive, since “gravitational
charges” always have the same sign, while the gravitational constant leads to
attraction (see (17.4)).
Certainly, ... (17.3)
Similar considerations apply to gravitational forces; in fact, “gravitational
mass” could also be termed “gravitational charge”, although an essential
difference from electric charges...
... decayed
from a state without any angular momentum. We assume that the decay products
are two particles, which travel diametrically away from each other in opposite di-
rections, and which are always correlated ... measuring apparatus on the
r.h.s. prepares a spin state with a value
2
in a certain direction, then a simultanous
measurement on the opposite side, performed with a si...
... ap-
proximation, usually called mean field approximation, by replacing a sum
of bilinear operators by a self-consistent temperature-dependent linear ap-
proximation in which fluctuations are neglected. ... we have seen that thermal fluctuations are im-
portant in the neighborhood of the critical temperature of a second-order
phase transition, i.e. near the critical temperature of a liqui...
... Vector as an Additional Conserved Quantity 39
7 The Rutherford Scattering Cross-section 41
8 Lagrange Formalism I: Lagrangian and Hamiltonian 45
8.1 The Lagrangian Function; Lagrangian Equations
of ... Current Loops and their Equivalent Magnetic
Dipoles 149
18.5 GyromagneticRatioandSpinMagnetism 151
19 Maxwell’s Equations I: Faraday’s and Maxwell’s Laws 153
19.1 Faraday’s Law of Induction and...
... Experiment;
LiquefactionofAir 319
41.7 Adiabatic ExpansionofanIdealGas 324
42 Phase Changes, van der Waals Theory
and Related Topics 327
42.1 VanderWaals Theory 327
42.2 Magnetic Phase Changes; The Arrott Equation. ... Quantum Mechanics: Retrospect and Prospect 293
38 Appendix: “Mutual Preparation Algorithm”
for Quantum Cryptography 297
Part I
Mechanics and Basic Relativity
4 1 Space and Ti...
... 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 equivalent to ... the planet covers equal areas in
equal time intervals.
3) The ratio T
2
/a
3
,whereT is the time period and a the major principal
axis of the ellipse, is constant for all planets (of the so...