Lectures on Quantum Mechanics for Mathematics Students by L. D. Faddeev and O. A. Yakubovskii in pdf

 Lectures on Quantum Mechanics for Mathematics Students by L. D. Faddeev and O. A. Yakubovskii in pdf

this is the book Lectures on Quantum Mechanics for Mathematics Students in pdf written  by L. D. Faddeev and O. A. Yakubovskii, published by American Mathematical Society, 2009  of professors of  science faculties  universities  .

   

Information about the book

Language of the book: English language

Book Title: Lectures on Quantum Mechanics for Mathematics Students

Scriptwriter: by L. D. Faddeev and O. A. Yakubovskii

Year of printing:   American Mathematical Society, 2009

File Format:PDF

Number of chapters: 52 CHAPTER

Number of pages: 234 pages

File Size: 11,10 MB

Contents

§1. The algebra of observables in classical mechanics 

§2. States 

§3. Liouville’s theorem, and two pictures of motion in

classical mechanics 

§4. Physical bases of quantum mechanics 

§5. A finite-dimensional model of quantum mechanics 

§6. States in quantum mechanics 

§7. Heisenberg uncertainty relations 

§8. Physical meaning of the eigenvalues and eigenvectors of

observables 

§9. Two pictures of motion in quantum mechanics. The

Schr¨odinger equation. Stationary states 

§10. Quantum mechanics of real systems. The Heisenberg

commutation relations 

§11. Coordinate and momentum representations 

§12. “Eigenfunctions” of the operators Q and P 

§13. The energy, the angular momentum, and other examples

of observables 

§14. The interconnection between quantum and classical

mechanics. Passage to the limit from quantum

mechanics to classical mechanics 

§15. One-dimensional problems of quantum mechanics. A

free one-dimensional particle 

§16. The harmonic oscillator 

§17. The problem of the oscillator in the coordinate

representation

§18. Representation of the states of a one-dimensional

particle in the sequence space l2 

§19. Representation of the states for a one-dimensional

particle in the space D of entire analytic functions 

§20. The general case of one-dimensional motion 

§21. Three-dimensional problems in quantum mechanics. A

three-dimensional free particle 

§22. A three-dimensional particle in a potential field 

§23. Angular momentum 

§24. The rotation group 

§25. Representations of the rotation group

§26. Spherically symmetric operators 

§27. Representation of rotations by 2 × 2 unitary matrices 

§28. Representation of the rotation group on a space of entire

analytic functions of two complex variables 

§29. Uniqueness of the representations Dj 

§30. Representations of the rotation group on the space

L2(S2). Spherical functions 

§31. The radial Schr¨odinger equation 

§32. The hydrogen atom. The alkali metal atoms 

§33. Perturbation theory 

§34. The variational principle 

§35. Scattering theory. Physical formulation of the problem 

§36. Scattering of a one-dimensional particle by a potential

barrier 

§37. Physical meaning of the solutions ψ1 and ψ2 

§38. Scattering by a rectangular barrier 

§39. Scattering by a potential center 

§40. Motion of wave packets in a central force field 

§41. The integral equation of scattering theory 

§42. Derivation of a formula for the cross-section 

§43. Abstract scattering theory 

§44. Properties of commuting operators 

§45. Representation of the state space with respect to a

complete set of observables 

§46. Spin 

§47. Spin of a system of two electrons 

§48. Systems of many particles. The identity principle

§49. Symmetry of the coordinate wave functions of a system

of two electrons. The helium atom 

§50. Multi-electronatoms. One-electronapproximation 

§51. The self-consistent field equations 

§52. Mendeleev’s periodic system of the elements

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