Elementary Derivation of Heisenbergs Uncertainty Relation

We consider a wave packet of finite width. For the sake of simplicity we represent its amplitude at any moment by a Gauss error function (such as actually occurs in the ground state of the harmonic oscillator, Appendix XXXII, p. 343)  

This integral is transformed by the substitution x/a + Trixa — y into the Gauss integral  

Tli( (listril)ution of the elementary waves composing the wave packet f(x) is again a Gauss function with the half width b Putting 

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