Vote on which university has the correct normalized quantum harmonic oscillator equation!!!(adsbygoogle = window.adsbygoogle || []).push({});

Is it University #1

Georgia State University and the Hyperphysics site presented by the physics department.

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hosc2.html#c1

[tex]\psi_n \left( y \right) = \left( \frac {\alpha}{{\pi}} \right) ^ \frac{1}{{4}} \frac{1}{{\sqrt{2^nn!}}}H_n\left(y\right)e^{\frac{-y^2}{{2}}}[/tex]

Where [tex]y = \sqrt{\alpha} x [/tex]

and [tex]\alpha = \frac{m\omega}{{\hbar}}[/tex]

Is it University #2

Oxford University with a paper from the Physical Chemistry department

http://physchem.ox.ac.uk/~hill/tutorials/qm2_tutorial/sho_series.pdf [Broken]

[tex]\psi_v\left(y\right) = \frac{1}{{\sqrt{\pi}{{2^vv!}}}}H_v\left(y\right)e^{\frac{-y^2}{{2}}}[/tex]

Where [tex]y = \sqrt{\frac{m\omega}{{\hbar}}}x[/tex]

Or is it University #3

University of Glasgow with a paper from the Physics department

http://www.physics.gla.ac.uk/~dmiller/lectures/P409M_Miller_2008_section4.pdf [Broken]

[tex]\psi_n \left( x \right) = \sqrt{\frac{\alpha}{{\sqrt{\pi}2^nn!}}}H_n\left(ax\right)e^\frac{-\alpha^2x^2}{{2}}[/tex]

Where y = [tex]\alpha x[/tex]

and [tex]\alpha = \sqrt{\frac{m\omega}{{\hbar}}}[/tex]

The normalizing constant is different for each equation so they all can not be the same.

When you cast your vote it would be helpful to others if you would justify your selection.

Thanks for participating.

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