the new fuels with magnecular structure - Institute for Basic Research

THE NEW FUELS WITH MAGNECULAR STRUCTURE 171
0.5
0.4
psi
0.3
0.2
0.1
0
0 1 2 3 4 5 6
r, a.u.
Figure A1. Landau’s ground state wave function of a single electron, ψ 000 (solid curve),
Eq. (A.8), in a strong external magnetic field B = B 0 = 2.4 · 10 9 Gauss, as function of the
distance r in cylindrical coordinates, and (for a comparison) the hydrogen ground state wave
function (at zero external magnetic field), (1/ √ π)e −r/a 0
(dashed curve), as function of the distance
r in spherical coordinates. The associated probability densities are shown in Fig. A2;
1 a.u. = a 0 = 0.53 · 10 −8 cm.
0.6
0.5
0.4
Landau
0.3
0.2
0.1
0
0 1 2 3 4 5 6
r, a.u.
Figure A2. Probability density for the case of Landau’s ground state of a single electron,
2πr|ψ 000| 2 (solid curve), Eq. (A.8), in a strong external magnetic field B = B 0 = 2.4 · 10 9
Gauss, as a function of the distance r in cylindrical coordinates, and (for a comparison)
the probability density of the hydrogen atom ground state (at zero external magnetic field),
4πr 2 |(1/ √ π)e −r/a 0
| 2 (dashed curve), as function of the distance r in spherical coordinates. The
associated wave functions are shown in Fig. A1; 1 a.u. = 0.53 · 10 −8 cm.
Figure A1 depicts Landau’s ground state wave function of a single electron,
ψ 000 , in the strong external magnetic field B = B 0 = 2.4·10 9 Gauss (R 0 = 1 a.u.),
and (for a comparison) of the hydrogen ground state wave function, at zero
external magnetic field, (1/ √ π)e −r/a 0
. Figures A2 and A3 display the associated
probability density of the electron as a function of the distance r from the center
of the orbit, the radius of which is about 1 a.u.