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Gaussian wave packet exploration
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Module 1
Mathematical Preliminaries
1
Complex Numbers: Euler's Formula and Exponential Form
Manipulate complex numbers in exponential form and apply Euler's formula.
2
Gaussian Integral Evaluation
Evaluate definite and indefinite Gaussian integrals using standard techniques.
3
Fourier Transforms of Simple Functions
Compute Fourier transforms and inverse Fourier transforms of simple functions, including Gaussians.
4
Solving Second-Order Linear Homogeneous ODEs with Constant Coefficients
Solve second-order linear homogeneous ordinary differential equations with constant coefficients.
5
Expectation and Standard Deviation for Continuous Distributions
Compute expectation values and standard deviations for continuous probability distributions.
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