I wish to graph a couple of the waveforms of a harmonic oscillator. I have consulted several resources and have found two that I like but the final equation differs even though they are both labeled normalized harmonic oscillator wavefunction. The first reference explains how the harmonic oscillator function is determined and the harmonic equation is at the very bottom of this 3 page document. http://physchem.ox.ac.uk/~hill/tutorials/qm2_tutorial/sho_series.pdf The second reference only presents the harmonic equation after a very brief discussion and it too is at the bottom of a 1 page display. http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hosc2.html#c1 The difference is the first term after the equate which is: (alpha/pi)^1/4. This term does not appear in the first reference but does appear in the second. Also the constants just before the Hermite function differ. Does anybody know why there is a difference between these two equations and how the difference occured?