FOUNDATIONS OF QUANTUM MECHANICS

LIST OF FIGURES
III. 1 A discontinuous measure for dim H = 2 . . . . . . . . . 48
III. 2 A rotated unit vector in the xz - plane . . . . . . . . . . 68
III. 3 Spin up for particle 1 along ⃗a, for particle 2 along ⃗ b . . . . . . 73
IV. 1 Heisenberg’s γ - microscope . . . . . . . . . . . . 79
IV. 2 The double slit interference experiment (Bohr 1949 ) . . . . . . 89
IV. 3 Contexts of measurement in which the interference of the particles is visible,
and those in which the recoil of the screen is visible, exclude each other. (Bohr
1949 ) . . . . . . . . . . . . . . . . . . 90
IV. 4 Several perfect crystal neutron interferometers (Rauch and Werner 2000 ) . 93
IV. 5 The interference pattern in the neutron interferometer is acquired by measuring
the intensity in the detectors at a variable optical path length difference. . 94
IV. 6 The probability distribution in position for a slit of width 2 a . . . . 101
IV. 7 The diffraction pattern for a small slit of width 2 a . . . . . . . 101
IV. 8 The probability distribution in position for a double slit, 2 a is the width of each
slit and 2 A the distance between the slits . . . . . . . . . 104
IV. 9 The interference pattern for the double slit . . . . . . . . . 104
IV. 10 Moving screen . . . . . . . . . . . . . . . . 106
V. 1 A solution for dim H = 2 . . . . . . . . . . . . . 117
V. 2 a) Kochen - Specker diagram b) Conway - Kochen diagram . . . . 118
V. 3 M.C. Escher, Waterfall. Consider the 3 interpenetrating cubes on the top of
the left pillar. Each cube has 4 lines from the mutual center to its vertices, 6
lines to the centers of its edges, and 3 lines to the centers of its faces. Three of
the lines are shared by all three cubes, giving 3 · (4 + 6 + 3 ) − 6 = 33 lines.
These are Peres’ vectors. (Text Meyer 2003 ) . . . . . . . . 119
V. 4 µ(P i ) = cos 2 θ . . . . . . . . . . . . . . . 120
VI. 1
VI. 2
The quantum potential for the two slit system as viewed from the screen, under
assumption of a Gaussian distribution at the slits (Bohm 1989 ) . . . 131
A simulation of the double slit experiment in Bohmian mechanics. Each particle
follows a certain path between the slits and the photographic plate. All
particles coming from the upper slit arrive at the upper half of the photographic
plate, likewise for the lower slit and lower half of the plate. The twists in the
paths are caused by the quantum potential U. (Vigier et al. 1987 ) . . . 132
VII. 1 Thought experiment of Einstein, Podolsky and Rosen on the singlet . . . 140
VII. 2 A configuration in which the spin quantities violate the Bell inequality . . 142
VII. 3 The Bell inequality violated for every acute angle ϕ . . . . . . 143
VII. 4 the configuration giving the largest violation of the Bell inequality (all vectors
in the same plane) . . . . . . . . . . . . . . . 143