- #1
astro_girl
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To illustrate the abstract reduction to dimensionless quantities apply it to the harmonic oscillator
V(x) = (m \omega^2 x^2) / 2
using x_0 = sqrt(h-bar/(m \omega))
and fi nd a dimensionless Schrodinger equation. Translate the known solutions to the Schrodinger
equation for the harmonic oscillator E_n = (n + 1/2)h-bar\omega
into the allowed energies ~E of the dimensionless Schrodinger equation.
I know this has to do with dimensional analysis, but I was sick when we had that class, and I've been searching for help on the internet the whole day without any luck. I don't think it is too difficult, I just don't really get what I have to do.
I guess the \omega and the m have to go, but how?
V(x) = (m \omega^2 x^2) / 2
using x_0 = sqrt(h-bar/(m \omega))
and fi nd a dimensionless Schrodinger equation. Translate the known solutions to the Schrodinger
equation for the harmonic oscillator E_n = (n + 1/2)h-bar\omega
into the allowed energies ~E of the dimensionless Schrodinger equation.
I know this has to do with dimensional analysis, but I was sick when we had that class, and I've been searching for help on the internet the whole day without any luck. I don't think it is too difficult, I just don't really get what I have to do.
I guess the \omega and the m have to go, but how?