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Wave Functions - Weber State University

2. WavefunctionsCopyrightc 2015 2016, Daniel V. SchroederTo create a precise theory of the wave properties of particles and of measurementprobabilities, we introduce the concept of awavefunction: a function of space thatencodes the current State of a now, we ll assume that the system consists of a single particle living in aone-dimensional universe. (We ll generalize to more complicated systems in a fewweeks.) Then, if this were aclassicalparticle, the State of the system wouldconsist of just two numbers: its positionxand its momentumpx(or velocityvx,which you can easily calculate from the momentum). For aquantumparticle, thestate instead consists of thewavefunction (x), a whole infinity of numbers (onefor eachx).

a mechanical wave or an electromagnetic wave is proportional to the square of the wave amplitude. Here is a plot of the square of our ve-bump wavefunction: ... The simplest periodic function would be a sine or a cosine, which would look like this: A long wavelength would correspond to a small momentum, and a short wavelength

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