I am working with the following harmonic oscillator formula.(adsbygoogle = window.adsbygoogle || []).push({});

[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]

I can not find a non-circular definition for [tex]\omega[/tex] or k.

For a quantum harmonic oscillator the only definitions for [tex]\omega[/tex] and k that I have found are

[tex]

\omega = \sqrt\frac{k}{{mass}}

[/tex]

[tex]

k = mass*\omega^2

[/tex]

which are circular.

Does anybody have a different definition for [tex]\omega[/tex] or k that works in the above quantum harmonic oscillator?

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# Quantum Harmonic Oscillator

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