Notes on quantum mechanics
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Notes on quantum mechanics
Notes on Quantum MechanicsK. SchultenDepartment of Physics and Beckman Institute University of Illinois at Urbana-Champaign 405 N. Mathews Street, Urb Notes on quantum mechanics bana, IL 61801 USA(April 18, 2000)PrefaceiPrefaceThe following notes introduce Quantum Mechanics at ail advanced level addressing students of Physics, Mathematics, Chemistry and Electrical Engineering. The aim is to put mathematical concepts and techniques like the path integral, algebraic technique Notes on quantum mechanics s, Lie algebras and representation theory at the readers disposal. For this purpose we attempt to motivate the various physical and mathematical conceNotes on quantum mechanics
pts as well as provide detailed derivations and complete sample calculations. We have made every effort to include in the derivations all assumptions Notes on Quantum MechanicsK. SchultenDepartment of Physics and Beckman Institute University of Illinois at Urbana-Champaign 405 N. Mathews Street, Urb Notes on quantum mechanics s references accompanying the mathematical derivations such that the intelligent and diligent reader should he able to follow the text with relative ease, in particular, also when mathematically difficult material is presented. In fact, the author’s driving force has been his desire to pave rhe read Notes on quantum mechanics er’s way into territories unchartered previously in most introductory textbooks, since few practitioners feel obliged to ease access lo then held. AlsNotes on quantum mechanics
o the author embraced enthusiastically the potential of the 1LX typesetting language to enhance the presentation of equations as to make the logical pNotes on Quantum MechanicsK. SchultenDepartment of Physics and Beckman Institute University of Illinois at Urbana-Champaign 405 N. Mathews Street, Urb Notes on quantum mechanics , that even though these notes attempt to serve rhe reader as much as was possible for rhe author, the main effort to follow the text and to master the material is left to the reader.The notes start out in Section 1 with a brief review of Classical Mechanics in the l^agrange formulation and build on Notes on quantum mechanics this to introduce in .Section 2 Quantum Mechanics in the closely related path integral formulation. In Section 3 the Schrodinger equation is derivedNotes on quantum mechanics
and used as an alternative description of continuous quantum systems. Section 4 is devoted to a detailed presentation of the harmonic oscillator, intrNotes on Quantum MechanicsK. SchultenDepartment of Physics and Beckman Institute University of Illinois at Urbana-Champaign 405 N. Mathews Street, Urb Notes on quantum mechanics of the 3-dimensional rotation group and the group SU(2) presenting Lie algebra and Lie group techniques and applying the methods to the theory of angular momentum, of the spin of single J>articles and of angular momenta and spins of composite systems. In Section 6 we present the theory of many boso Notes on quantum mechanics n and many fermion systems in a formulation exploiting the algebra of the associated creation and annihilation operators. Section 7 provides an introdNotes on quantum mechanics
uction to Relativistiã Quantum Mechanics which builds on the representation theory of the Lorentz group and its complex relative S7(2. C). Tills sectiNotes on Quantum MechanicsK. SchultenDepartment of Physics and Beckman Institute University of Illinois at Urbana-Champaign 405 N. Mathews Street, Urb Notes on quantum mechanics Special Relativity and Quantum Mechanics.The notes are in a stage of continuing development, various sections, e.g., on the semiclassical approximation, on the Hilbert space structure of Quantum Mechanics, on scattering theory, on perturbation theory, on Stochastic Quantum Mechanics, and on the gro Notes on quantum mechanics up theory of elementary particles will be added as well as the existing sections expanded. However, al the present stage the notes, for the topics covNotes on quantum mechanics
ered, should be complete enough to serve the reader.The author would like to thank Markus Vim Almsick and lleichi Chan for help with these notes. The Notes on Quantum MechanicsK. SchultenDepartment of Physics and Beckman Institute University of Illinois at Urbana-Champaign 405 N. Mathews Street, Urb Notes on quantum mechanics fort and a great pleasure.These notes were produced entirely on a Miicmlush 11 computer using the TeX typesetting system, Textures, Mathematics and Adobe Illustrator.Klaus SciiultcuUniversity of Illinois at Urbana Champaign33451www.pdfgrip.comiiPrefaceWWW pdfgrip.comContents1Lagrangian Mechanics11.1 Notes on quantum mechanics Basics of Variational Calculus.............................................. 11.2Lagrangian Mechanics.................................................Notes on quantum mechanics
....... 41.3Symmetry Properties in Lagrangian Mechanics................................. 72Quant tun Mechanical Path Integral112.1The Double Slit ExpeNotes on Quantum MechanicsK. SchultenDepartment of Physics and Beckman Institute University of Illinois at Urbana-Champaign 405 N. Mathews Street, Urb Notes on quantum mechanics valuate the Path Integral.......................................... 142.4Propagator for a Free Particle............................................. 142.5Propagator for a Quadratic Lagrangian ..................................... 222.6Wave Packet Moving in Homogeneous Force Field ................... Notes on quantum mechanics ...........252.7Stationary Slates of t he Harmonic Oscillator ........................... '.Ì43The Schrodinger Equation513.1Derivation of the SchrodinNotes on quantum mechanics
ger Equation .................................... 513.2Boundary Conditions........................................................ 53Notes on Quantum MechanicsK. SchultenDepartment of Physics and Beckman Institute University of Illinois at Urbana-Champaign 405 N. Mathews Street, UrbNotes on Quantum MechanicsK. SchultenDepartment of Physics and Beckman Institute University of Illinois at Urbana-Champaign 405 N. Mathews Street, UrbGọi ngay
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