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''' Welcome to the Quantum Mechanics A PHY5645 Fall2008/2009'''
''' Welcome to the Quantum Mechanics A PHY5645 Fall2008/2009'''
[[Image:SchrodEq.png|thumb|550px|Schrodinger equation. The most fundamental equation of quantum mechanics which describes the rule according to which a state <math>|\Psi\rangle</math> evolves in time.
[[Image:SchrodEq.png|thumb|550px|<b>[[Schrödinger Equation]]</b><br/>The most fundamental equation of quantum mechanics; given a Hamiltonian <math>\mathcal{H}</math>, it describes how a state <math>|\Psi\rangle</math> evolves in time.]]
]]  
 
This is the first semester of a two-semester graduate level sequence, the second being [[phy5646|PHY5646 Quantum B]]. Its goal is to explain the concepts and mathematical methods of Quantum Mechanics, and to prepare a student to solve quantum mechanics problems arising in different physical applications. The emphasis of the courses is equally on conceptual grasp of the subject as well as on problem solving. This sequence of courses builds the foundation for more advanced courses and graduate research in experimental or theoretical physics.  
This is the first semester of a two-semester graduate level sequence, the second being [[phy5646|PHY5646 Quantum B]]. Its goal is to explain the concepts and mathematical methods of Quantum Mechanics, and to prepare a student to solve quantum mechanics problems arising in different physical applications. The emphasis of the courses is equally on conceptual grasp of the subject as well as on problem solving. This sequence of courses builds the foundation for more advanced courses and graduate research in experimental or theoretical physics.  
   
   
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== Outline of the Course ==
== Outline of the Course ==


<b>[[Physical Basis of Quantum Mechanics|Chapter 1: Physical Basis of Quantum Mechanics]]</b>
<b>Chapter 1: [[Physical Basis of Quantum Mechanics]]</b>


* [[Basic Concepts and Theory of Motion]]
* [[Basic Concepts and Theory of Motion]]
* [[UV Catastrophe (Black Body Radiation)]]
* [[UV Catastrophe (Black-Body Radiation)]]
* [[Photoelectric Effect]]
* [[Photoelectric Effect]]
* [[Stability of Matter]]
* [[Stability of Matter]]
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<b>[[Schrödinger equation|Chapter 2: Schrödinger Equation]]</b>  
<b>Chapter 2: [[Schrödinger Equation]]</b>  
   
   
* [[Original Idea of Schrödinger Equation]]
* [[Brief Derivation of Schrödinger Equation]]
* [[Brief deviation of Schrodinger Equation|Brief Derivation of Schrodinger Equation]]
* [[Relation Between the Wave Function and Probability Density]]
* [[Stationary states|Stationary States]]
* [[Stationary States]]
* [[Conservation of probability|Conservation of Probability]]
* [[Heisenberg Uncertainty Principle]]
* [[States, Dirac bra-ket notation|States, Dirac Bra-Ket Notation]]
* [[Heisenberg Uncertainty relations|Heisenberg Uncertainty Relations]]
* [[Some Consequences of the Uncertainty Principle]]
* [[Some Consequences of the Uncertainty Principle]]




<b>[[Motion in one dimension|Chapter 3: Motion in One Dimension]]</b>  
<b>Chapter 3: [[Operators, Eigenfunctions, and Symmetry]]</b>
* [[1D bound states|1D Bound States]]
* [[The Dirac Delta function potential|The Dirac Delta Function Potential]]
* [[Scattering states|Scattering States]]
* [[Oscillation theorem|Oscillation Theorem]]
* [[Transmission-Reflection, S-matrix|Transmission-Reflection, S-matrix]]
* [[Motion in a periodic potential|Motion in a Periodic Potential]]
* [[Summary of 1D Systems]]


* [[Linear Vector Spaces and Operators]]
* [[Commutation Relations and Simultaneous Eigenvalues]]
* [[The Schrödinger Equation in Dirac Notation]]
* [[Transformations of Operators and Symmetry]]
* [[Time Evolution of Expectation Values and Ehrenfest's Theorem]]


<b>[[Operators, eigenfunctions, symmetry, and time evolution|Chapter 4: Operators, Eigenfunctions, Symmetry, and Time Evolution]]</b>


* [[Linear Vector Space and Operators]]
<b>Chapter 4: [[Motion in One Dimension]]</b>
* [[Commutation relations and simultaneous eigenvalues|Commutation Relations and Simultaneous Eigenvalues]]
* [[Symmetry and Its Role in Quantum Mechanics|Symmetry and its Role in Quantum Mechanics]]
* [[One-Dimensional Bound States]]
* [[Ehrenfest's Theorem]]
* [[Oscillation Theorem]]
* [[Heisenberg and interaction picture: Equations of motion for operators|Heisenberg and Interaction Pictures: Equations of Motion for Operators]]
* [[The Dirac Delta Function Potential]]
* [[The Interaction Picture]]
* [[Scattering States, Transmission and Reflection]]
* [[The Virial Theorem]]
* [[Motion in a Periodic Potential]]
* [[Feynman path integrals|Feynman Path Integrals]]
* [[Summary of One-Dimensional Systems]]
* [[Problems]]




<b>[[Discrete_eigenvalues_and_bound_states._Harmonic_oscillator_and_WKB_approximation|Chapter 5: Discrete Eigenvalues and Bound States]]</b>
<b>Chapter 5: [[Discrete Eigenvalues and Bound States - The Harmonic Oscillator and the WKB Approximation]]</b>


* [[Harmonic oscillator spectrum and eigenstates|Harmonic Oscillator Spectrum and Eigenstates]]
* [[Harmonic Oscillator Spectrum and Eigenstates]]
* [[Analytical Method for Solving the Simple Harmonic Oscillator]]
* [[Analytical Method for Solving the Simple Harmonic Oscillator]]
* [[Coherent states|Coherent States]]
* [[Coherent States]]
* [[Feynman path integral evaluation of the propagator|Feynman Path Integral Evaluation of the Propagator]]
* [[Charged Particles in an Electromagnetic Field]]
* [[Motion in electromagnetic field|Motion in Electromagnetic Field]]
* [[WKB Approximation]]
* [[WKB Approximation]]




<b>[[Path Integral Evaluation of the Free-Particle Propagator|Chapter 6: Path Integral Evaluation of the Free-Particle Propagator]]</b>
<b>Chapter 6: [[Time Evolution and the Pictures of Quantum Mechanics]]</b>


* [[Saddle point action|Saddle Point Action]]
* [[The Heisenberg Picture: Equations of Motion for Operators]]
* [[Harmonic fluctuations|Harmonic Fluctuations]]
* [[The Interaction Picture]]
* [[The Virial Theorem]]




<b>[[Angular momentum|Chapter 7: Angular Momentum]]</b>
<b>Chapter 7: [[Angular Momentum]]</b>
   
   
* [[Commutation relations|Commutation Relations]]
* [[Commutation Relations]]
* [[Angular momentum as a generator of rotations in 3D|Angular Momentum as a Generator of Rotations in 3D]]
* [[Angular Momentum as a Generator of Rotations in 3D]]
* [[Spherical Coordinates]]
* [[Spherical Coordinates]]
* [[Eigenvalue quantization|Eigenvalue Quantization]]
* [[Eigenvalue Quantization]]
* [[Orbital angular momentum eigenfunctions|Orbital Angular Momentum Eigenfunctions]]
* [[Orbital Angular Momentum Eigenfunctions]]
* [[Problems on Angular Momentum]]




<b>[[Central forces|Chapter 8: Central Forces]]</b>  
<b>Chapter 8: [[Central Forces]]</b>  
   
   
* [[Generalized derivation|Generalized Derivation]]
* [[General Formalism]]
* [[Free particle in spherical coordinates|Free Particle in Spherical Coordinates]]
* [[Free Particle in Spherical Coordinates]]
* [[Spherical well|Spherical Well]]
* [[Spherical Well]]
* [[Isotropic Harmonic Oscillator]]
* [[Isotropic Harmonic Oscillator]]
* [[Hydrogen atom|Hydrogen Atom]]
* [[Hydrogen Atom]]
* [[WKB in spherical coordinates|WKB in Spherical Coordinates]]
* [[WKB in Spherical Coordinates]]
 
 
<b>Chapter 9: [[The Path Integral Formulation of Quantum Mechanics]]</b>
 
* [[Feynman Path Integrals]]
* [[The Free-Particle Propagator]]
* [[Propagator for the Harmonic Oscillator]]




<b>[[Continuous eigenvalues and collision theory|Chapter 9: Continuous Eigenvalues and Collision Theory]]</b>  
<b>Chapter 10: [[Continuous Eigenvalues and Collision Theory]]</b>  
   
   
* [[Differential cross-section and the Green's function formulation of scattering|Differential Cross-Section and the Green's Function Formulation of Scattering]]
* [[Differential Cross Section and the Green's Function Formulation of Scattering]]
* [[Central potential scattering and phase shifts|Central Potential Scattering and Phase Shifts]]
* [[Central Potential Scattering and Phase Shifts]]
* [[Born approximation and examples of cross-section calculations|Born Approximation and Examples of Cross-Section Calculations]]
* [[Coulomb Potential Scattering]]
* [[Coulomb potential scattering|Coulomb Potential Scattering]]
* [[Two particle scattering|Two-Particle Scattering]]

Latest revision as of 14:59, 8 April 2014

Quantum.png

Welcome to the Quantum Mechanics A PHY5645 Fall2008/2009

Schrödinger Equation
The most fundamental equation of quantum mechanics; given a Hamiltonian , it describes how a state evolves in time.

This is the first semester of a two-semester graduate level sequence, the second being PHY5646 Quantum B. Its goal is to explain the concepts and mathematical methods of Quantum Mechanics, and to prepare a student to solve quantum mechanics problems arising in different physical applications. The emphasis of the courses is equally on conceptual grasp of the subject as well as on problem solving. This sequence of courses builds the foundation for more advanced courses and graduate research in experimental or theoretical physics.

The key component of the course is the collaborative student contribution to the course Wiki-textbook. Each team of students is responsible for BOTH writing the assigned chapter AND editing chapters of others.

Team assignments: Fall 2009 student teams

Fall 2009 Midterm is October 15

Outline of the Course

Chapter 1: Physical Basis of Quantum Mechanics


Chapter 2: Schrödinger Equation


Chapter 3: Operators, Eigenfunctions, and Symmetry


Chapter 4: Motion in One Dimension


Chapter 5: Discrete Eigenvalues and Bound States - The Harmonic Oscillator and the WKB Approximation


Chapter 6: Time Evolution and the Pictures of Quantum Mechanics


Chapter 7: Angular Momentum


Chapter 8: Central Forces


Chapter 9: The Path Integral Formulation of Quantum Mechanics


Chapter 10: Continuous Eigenvalues and Collision Theory

Retrieved from "http://wiki.physics.fsu.edu/index.php?title=Phy5645&oldid=15857"