1. Matrix mechanics
1.1. Linear vector spaces
1.1.1.Dirac’s notation
1.1.2.Orthonormal basis
1.2. Matrices
1.2.1.Basic principles
1.2.2.Matrix transformations
1.2.3.Diagonalisation of a matrix, eigenvalues and eigenvectors
1.2.4.Unitary matrix
1.2.5.Diagonalization of two commuting matrices
1.3. Generalization to infinite dimensional Hilbert-space
1.3.1.Coordinate and momentum spaces
1.3.2.Countable basis
1.3.3.Continuum and discrete spectra together
1.4. Basic principles and postulates in the matrix form
1.5. Two-level system
1.5.1.Notations
1.5.2.New eigenstates and eigenvalues
1.5.3.Oscillations between unpertubed states
1.6. Matrix elements of the gradient operator
1.7. Harmonic oscillator in the lgebraic form
1.7.1.Creation and annihilation operators
1.7.2.Normalized eigenvectors
1.7.3.Operators in matrix representation
1.7.4.Wave functions
2. Angular momentum and spin
2.1. Group theory and theory of representations of groups
2.1.1.Group axioms and representations of groups
2.1.2.Group of rotations
2.1.3.Infinitesimal rotation
2.1.4.Rotation-operator PR
2.1.5.Hamilton operator in a symmetric rotation
2.2. Irreduciple representations of the rotation group
2.2.1.Diagonalization of operators J2 ja Jz
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2.2.2.Matrix elements of operators J+ja J2.2.3.Matrix representations of rotation group
2.3. Rigid-body rotation in quantum mechanics
2.3.1.Classical Hamiltonian
2.3.2.Quantum mechanics approach
2.4. Particle in an electromagnetic field
2.4.1.Classical Hamiltonian
2.4.2.Schrödinger equation
2.4.3.Zeeman-phenomenon in Hydrogen atom
2.5. Electron spin
2.5.1.Mathematical handling of the spin
2.6. Total angular momentum
2.6.1.Coupling of angular momenta
2.7. Fine structure of spectra
2.7.1.Thomas- or Ls-term in atoms
2.7.2.Expectation values
2.7.3.Relativistic p4=8m3c2 correction
2.7.4.Virial teorem
2.7.5.Hellman-Feynman teorem
3. Hydrogen molecule ion and chemical bonding
4. Coupled states of two particles with spin
4.1. States of the Helium-atom
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4.1.1.Lowest excited states
4.2. Two-electron atoms
4.3. Two spin-1/2 nuclei in a magnetic field (AB-spin system)
5. Time dependent Schröding equation
5.1. Stationary states
5.2. Time dependent perturbations
5.3. Harmonic perturbation: Fermi golden rule
5.4. Interaction of radiation and matter
5.4.1.Harmonic perturbation
5.4.2.Separation of center of mass
5.4.3.Intensity of the radiation
5.4.4.Dipole absorption ja induced emission
5.4.5.Spontaneous emission
5.4.6.Spontaneous dipole transition in 1D harmonic oscillator
5.4.7.Spontaneous dipole transition in Hydrogen atom
5.5. AB-spin system in an oscillation magnetic field
6. Scattering theory
6.1. Scattering by a potential wall in one dimension
6.2. Scattering of the wave packet by a potential step
6.2.1.Total reflection: E < V0
6.2.2.Partial reflection: E > V0
6.3. Free particle in three dimensions
6.3.1.Cartesian coordinates
6.3.2.Spherical coordinates
6.3.3.Bessel and Neuman functions
6.3.4.Expansion of the plane wave in spherical harmonics
6.4. Scattering by a short range central field
6.4.1.Scattering-amplitude and cross section
6.4.2.Partial wave expansion
6.5. Energy dependence of phase shifts
6.5.1..Low energy scattering
6.5.2. Scattering length
6.5.3. Scattering by a hard sphere
6.5.4. Scattering by an attractive potential
6.5.5. Effective range
6.5.6. Bound state and S-matrix
6.6. General formulation of the scattering theory
6.6.1. Integral equation of the scattering
6.6.2.Asymptotic behavior and the scattering amplitude
6.6.3.Connection to the partial wave expansion
6.7. Born approximation
6.7.1. Atomic scattering of fast electrons
6.7.2. Charge distribution in the electron scattering
6.7.3.The Born approximation and the partial wave expansion
6.8. Scattering of identical particles
6.8.1.Spin states in the two-particle scattering
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