Define the mass of the Chlorine atom in kilograms

m = 0.035453/(6.022*10^23)

Now compute the reduced mass

μ=m m /(m + m)

This is the vibrational frequency of Cl2 in reciprocal meters (wavenumbers)

(OverBar[ν])=56000.0

Define the speed of light in SI units

c=2.998*10^8

Using our constants and molecular parameters, compute k

k=(c(OverBar[ν]) 2 π)^2 μ

Define Planck’s constant, and ℏ

h = 6.626*10^-34

ℏ=h/(2 π)

Define the α term that is used in subsequent steps

α=(k μ/ℏ^2)^(1/2)

Define the normalization constant function

𝒩[n_] := 1/ (2^n Factorial[n])^(1/2) (α/π)^(1/4)

Now define the harmonic oscillator wavefunction

ψ[x_,n_]:= 𝒩[n] HermiteH[n,α^(1/2) x] Exp[-α x^2/2]

These next two lines define plot limits for the x-axis in meters

xvar1 = -1*10^-10

xvar2 = -xvar1

And this should plot the wavefunction

Plot[ψ[x,0],{x,xvar1,xvar2}, PlotRange -> Full]