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Contence
Prologue. A Bouncing Ball
1. Hertz Contact Problem
2. Impact
3. Sticking to Plane
4. Energy Losses
5. Duration of Bouncing
Tale 1. Pendulum and WKB Approximation
1. Adiabatic Pendulum
2. Precision of Adiabatic Invariant Conservation
3. Connected Pendulums
Tale 2. Waves on Shallow Water
1. KdV Equation
2. The Inverse Scattering Problem for Schroedinger Equation
and on Solutions of KdV
3. Solitons and their collisions
4. Appendix. Solitons.
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Tale 3. Supersymmetry or how to get a Square Root
from an Operator
1. Supersymmetry and Witten's Supersymmetric Mechanics.
2. A life case
3. Reectionless Potential
Tale 4. A Drunkard and Policemen
Tale 5. Dirac Monopole, a Quantum Top and Macroscopic Spin Tunneling
Tale 6. Kramers' Phase
1. A paradox with Balmer Formula
2. Laplace Method and a Regular Turning Point
3. Kramers' Phase for the Coulomb Potential.
Tale 7. Singularities and their Classication
Tale 8. Taylor Instability and Ship Waves
1. The Taylor Instability
2. Circles on the Water formed by a falling Stone
3. Trace of a Moving Boat.
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Tale 9. Hidden Symmetry of the Kepler Problem
1. Puzzle of Closed Orbits.
2. Fock's Sphere
3. Angular Momentum and Runge-Lentz Vector
4. Quntum Mechanics, Energy Levels, Accidental Degeneracy
and Wave Functions.
5. Appendix 1. Parabolic Coordinates
6. Appendix 2. Continuum, Fock's Hyperboloid, O(2; 1) Algebra and Eigenstates of Continuum
7. Appendix 3. Zero Energy.
Tale 10. Rates of Activation Processes, the Kramers'
problem of Escape from a Trap and the Wiener-Hopf
Method
1. Kramers' Problem
2. Two Kramers' regimes
3. Crossover between Regimes. Integral Equation.
4. Wiener-Hopf Method for Solution of Integral Equations
Tale 11. Collapse of a Bubble in the Water, Scaling and
the Qualitative Theory of Dierential Equations
1. Rayleigh Problem of Collapsing Bubbles.
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2. Compressibility and Self-similar Solutions
of Partial Dierential Equations.
Two Types of Self-similarity. Strong Explosion
3. Self-similarity of Second Type and Condition on Index.
Solution of the Rayleigh Problem in a Compressible Liquid.
Tale 12. Calculation of the Sums, Landau Diamagnetism and the de Haas-van Alfven Eect
1. Watson-Sommerfeld Method
2. Euler-Maclaurin Method and Substitution a Sum by an Integral.
3. Poisson Method and Extracting an Oscillatory Part from
the Sum.
Tale 13. Soccer-ball and the Finite Group Representations
1. Geometry of a Socker-Ball
2. Two examples.
3. Donor in Ge
4. Icosahedral Group and its Character Table
5. Electron Levels of the Fullerene Molecule.
6. Hueckel Model
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Tale 14 Painting of Polyhedrons or the Shubnikov Problem
1. Problem of stability of a painted gure.
2. The Indenbohm's Construction.
3. Superconductivity in Crystals and Zeros of the Gap Function.
Tale 15, dedicated to M.D.Spector, on Dirichlet Principle and Geodesic Lines
Tale 16. Variable Dimensionality and on Estimation of
the Critical Depth of Potential Well
Tale 17. Rainbows and Catastrophes
1. Geometric Optics.
2. Wave theory. Fringes. Airy Function.
3. General Catastrophes. Rainbow from Elliptic Drop.
4. Fringes from Elliptic Drop.
Tale 18. Abrikosov's Lattice, Sunowers, Pineapples,
Elliptic Functions and Modular forms
Tale 19. Molecular Rotations and the Berry Phase
Tale 20. Innities and Regularizations
1. Electron in magnetic eld and a random potential
2. Self-energy correction and its regularization
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Tale 21 on Shape of Galaxies
1. Plasma Oscillations and Jeans Instability
2. Plasma Waves in Two Dimensions in Magnetic Field and
Gallaxes
Tale 22 on Dendrite Growth.
1. Ivantzov's regime and the patern selection problem.
2. Surface tension and the singular perturbation method.
3. Regime selection
Tale 25 on Special Functions and Group Representations
beginenumerate
Hypergeometric function
Group SL2(R), its structure and subgroups
Lie algebra sl2(R).
SO(n) and Gegenbauer Polynomials.
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Tale 26. Can one heard the string shape. Inverse scattering problem.
Tale 27 on Three Particles Collision and Tree Particles
Bound State
Tale 28 on Singular Integral Equations
Tale 29 on Higher Order in Perturbation Theory
1. Ordinary Integral
2. Anharmonic Oscillator
3. QED
Tale 30 on Boundary Layer and Submerged Jet.
1. Viscous ow and Reynolds number. Boundary layer, separation lines and turbulent tail.
2. Prandtl equations.
3. A wing in a ow.
4. Submerged jet.
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Tale 31 on Stability of Propagating Fronts or ZeldovichBarenblatt Theorem
Tale 32 on Hotzmark Distribution
Tale 33 on Kaleidescope
Tale 34 on Skirmions
Tale 35 on Dice
Tale 36 on Gaussian Integrals, Grassmannian Variables,
Matrices and Determinants and on Super-symmetry.
Tale 37. Proton Decay, Zero Modes and Attiyah - Singer
Theorem
Tale 38. Once more on Innities and regularisations.
Quantum anomalies
Tale 39 on Fluctuation of Distribution Function
Tale 40 Lie Algebras and Dynamic Symmetry
of Elementary Particles
1. Neutron
2. Deuton
3. Strange Particles
4. Search of Right Theory
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Tale 41 by Shankar on Tiling
Tale 42 on Frenet Formulae and Hyper-spiral Structure
of DNA
Tale 43 on Waterfalls and Shock Waves
1. Coastal Waves and Geometrical Optics
2. Waterfall. Waves of decompression. Riemann invariants
3. Waterfall. Shock waves.
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The last fairy tale on
Examples
Answers to examples
Reference Guide
References
Index
NEW FAIRY TALES
Tale 45 Spin and Oscillator
Tale 46 Green Functions and Resistor's Networks
Tale 47 Curvo-linear Coordinates
Tale 48 2 in the exponent
Tale 49 Knotes, Fermions and Ising model.
Tale 50
Tale 51
Tale 52
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