GM Jackson Physics and Mathematics

Showing posts with label mathematical proof. Show all posts
Showing posts with label mathematical proof. Show all posts
Tuesday, June 11, 2019

A Perturbation Theory Proof

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To prove the validity of the perturbation expansion, let's start with a simple and obvious statement: It seems intuitive that a va...
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Saturday, February 24, 2018

An Amplitude Squared Equals a Probability--a Mathematical Proof

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Start with a wave: Add more waves. Waves are in and out of phase with each other (constructive and destructive interference): The ...
Saturday, October 14, 2017

Proving the Schwartz Inequality and Heisenberg's Uncertainty Principle

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In this post we once again derive the Heisenberg uncertainty principle, but this time we make use of the Schwartz inequality and the posit...
Wednesday, October 4, 2017

Proving the Dirac Delta Function, Etc.

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In this post we prove the Dirac Delta function and its sampling property. Here are the variables we need: So we ask, is equation 1 be...
Monday, September 18, 2017

Deriving the Fourier Transform

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In the field of quantum mechanics the Fourier transform shows the relationship between momentum/wave-number space, phi(k), and position sp...
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