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The definition of scattering cross section for waves is given and the interpretation as an area is explained.

Differential equation for orbits is solved. The orbits are shown to be conic sections. Kepler's three laws are proved. Some properties of hyperbolic orbits are derived.$\newcommand{\pp}[2][]{\frac{\partial#1}{\partial #2}} \newcommand{\PP}[2][]{\frac{\partial^2#1}{\partial #2^2}} \newcommand{\dd}[2][]{\frac{d#1}{d #2}} \newcommand{\DD}[2][]{\frac{d^2#1}{d #2^2}}$

Quantum Mechanics Lecture Notes -16 HOME PAGE
Spherically Symmetric Potential Problems

• General Properties of Spherically Symmetric Potentials
• Angular Momentum in Coordinate Representtaion
• Solution of Radial Equation
• Hyderogen Atom Energy Levels

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We discuss an example of particle in two dimensions in  a potential independent of \(\theta\). By working in plane polar coordinates, we show how solution of  equations of motion   can be reduced to quadratures.

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The energy eigenvalues and eigenfunctions are obtained for a free particle in one dimension. Properties and delta function normalization are discussed. It is shown that the energy eigenvalue must be positive. The free particle solution in three dimension is briefly given.

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