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). Quantum states are vastly more complicated, and interesting, thanclassical example wavefunctionFor example, if we draw thexaxis across the two-slit interference pattern illustratedin the previous lesson (and ignore the other two dimensions of space), then thewavefunction of each particle, just before it hits the detection screen, might looksomething like this:This

The function j (x)j2 is called the probability density, and I like to think of it as a function whose purpose in life is to be integrated. In order for the rule to work, ... where Ais the wave amplitude, ˚is a phase constant that determines where the cycles start, and k= 2ˇ= . Notice that the two components share the same A, ˚,

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  Functions, Waves, Wave function

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