Template:Quantum Mechanics A

Quantum Mechanics A

Schrödinger Equation The most fundamental equation of quantum mechanics; given a Hamiltonian ${\mathcal {H}}$, it describes how a state $|\Psi \rangle$ evolves in time.

Physical Basis of Quantum Mechanics

Basic Concepts and Theory of Motion UV Catastrophe (Black-Body Radiation) Photoelectric Effect Stability of Matter Double Slit Experiment Stern-Gerlach Experiment The Principle of Complementarity The Correspondence Principle The Philosophy of Quantum Theory

Schrödinger Equation

Original Idea of Schrödinger Equation Brief Derivation of Schrödinger Equation Stationary States Conservation of Probability States, Dirac Bra-Ket Notation Heisenberg Uncertainty Principle Some Consequences of the Uncertainty Principle

Motion in One Dimension

One-Dimensional Bound States The Dirac Delta Function Potential Scattering States Oscillation Theorem Transmission-Reflection, S-Matrix Motion in a Periodic Potential Summary of One-Dimensional Systems

Operators, Eigenfunctions, Symmetry, and Time Evolution

Linear Vector Spaces and Operators Commutation Relations and Simultaneous Eigenvalues Symmetry and Its Role in Quantum Mechanics Ehrenfest's Theorem Heisenberg and Interaction Pictures: Equations of Motion for Operators The Interaction Picture The Virial Theorem Feynman Path Integrals Problems

Discrete eigenvalues and bound states

Harmonic oscillator spectrum and eigenstates Analytical Method for Solving the Simple Harmonic Oscillator Coherent states Feynman path integral evaluation of the propagator Motion in electromagnetic field WKB Approximation

Path Integral Evaluation of the Free-Particle Propagator

Saddle point action Harmonic fluctuations

Angular momentum

Commutation relations Angular momentum as a generator of rotations in 3D Spherical Coordinates Eigenvalue quantization Orbital angular momentum eigenfunctions Problems on Angular Momentum

Central forces

Generalized derivation Free particle in spherical coordinates Spherical well Isotropic Harmonic Oscillator Hydrogen atom WKB in spherical coordinates

Continuous eigenvalues and collision theory

Differential cross-section and the Green's function formulation of scattering Central potential scattering and phase shifts Born approximation and examples of cross-section calculations Coulomb potential scattering Two particle scattering

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