Figures 2.12 hasse diagrams of several boolean and non-Boolean algebras 3.1 Positive potential vanishing at infinity Potential function tending to finite values asx →士 0 Potential well 111 3.4 Relation between two different inertial reference frames R and R'under Galilei transformations 3 3.5 Particle in a box of dimensiona Energy levels of a particle in a one-dimensional box 3.7 First three energy eigenfunctions for a one-dimensional particle confined in a box of dimension a 115 3.8 Beam Splitters as unitary operators 119 3.9 proiector as a residue of the closed contour in a complex plane 124 3.10 A graphical representation of the apparatus proposed by Bohr 4.1 Schematic and tric one-dir otential wells 4.2 Solution of Eq.(4.8) 143 4.3 Wave functions and probability densities for the first three eigenfunctions for the symmetric finite-well potential 1 4 Stepwise continuity Potential barrier 64 4.6 Closed surface used to compute the flux of J 4 Delta potential barrier 149 4.8 Classical tuming points and quantum tunneling 4. Tunneling of o-particles 4.10 Carbon atoms shown by scanning tunneling microscopy 153 411 Potential and energy levels of the harmonic oscillator 4.12 Eigenfunctions for the one-dimensional harmonic oscillator 162 4.13 Potential energy corresponding to a particle in a uniform field 1 4.14 Triangular well 167 4.15 A quantum particle with energy E enc ounters a potential step of heigh Vo<E 171 4.16 Rectangular potential barrier with finite width a 171 5 Representation of pure and mixed states on a sphere 187 61 Angular momentum of a classical particle 6. Levi-Civita tensor Relationship between rectangular and spherical coordinates 200 s-and p-states 206 6 Rigid rotato 6.6 Energy levels and transition frequencies for a rigid rotator 67 Cylindrical coordinates 212 Energy levels of the thre -dimensional ha monic oscillator 6.9 Levels in the spectrum of hydrogen atom 6.10 An electric dipole with charges +e and -e in an electric field gradient 218 6.1m Scheme of spin superposition in single-crystal neutron interferometry 223 6.12 Lande vectorial model for angul 227 xii Figures 2.12 Hasse diagrams of several Boolean and non-Boolean algebras 95 3.1 Positive potential vanishing at infinity 109 3.2 Potential function tending to finite values as x → ±∞ 110 3.3 Potential well 111 3.4 Relation between two different inertial reference frames R and R under Galilei transformations 112 3.5 Particle in a box of dimension a 113 3.6 Energy levels of a particle in a one-dimensional box 115 3.7 First three energy eigenfunctions for a one-dimensional particle confined in a box of dimension a 115 3.8 Beam Splitters as unitary operators 119 3.9 Projector as a residue of the closed contour in a complex plane 124 3.10 A graphical representation of the apparatus proposed by Bohr 133 4.1 Schematic and asymmetric one-dimensional potential wells 142 4.2 Solution of Eq. (4.8) 143 4.3 Wave functions and probability densities for the first three eigenfunctions for the symmetric finite-well potential 144 4.4 Stepwise continuity 145 4.5 Potential barrier 147 4.6 Closed surface used to compute the flux of J 148 4.7 Delta potential barrier 149 4.8 Classical turning points and quantum tunneling 151 4.9 Tunneling of α-particles 152 4.10 Carbon atoms shown by scanning tunneling microscopy 153 4.11 Potential and energy levels of the harmonic oscillator 154 4.12 Eigenfunctions for the one-dimensional harmonic oscillator 162 4.13 Potential energy corresponding to a particle in a uniform field 165 4.14 Triangular well 167 4.15 A quantum particle with energy E encounters a potential step of height V0 < E 171 4.16 Rectangular potential barrier with finite width a 171 5.1 Representation of pure and mixed states on a sphere 187 6.1 Angular momentum of a classical particle 194 6.2 Levi–Civita tensor 195 6.3 Relationship between rectangular and spherical coordinates 200 6.4 s- and p-states 206 6.5 Rigid rotator 207 6.6 Energy levels and transition frequencies for a rigid rotator 209 6.7 Cylindrical coordinates 212 6.8 Energy levels of the three-dimensional harmonic oscillator 215 6.9 Levels in the spectrum of hydrogen atom 218 6.10 An electric dipole with charges +e and −e in an electric field gradient 218 6.11 Scheme of spin superposition in single-crystal neutron interferometry 223 6.12 Landé vectorial model for angular momentum 227