In the Schrödinger wave equation, where does the $8\pi^2 m/h$ come from?
Where $m$ is the mass and $h$ is Planck's constant
I understand the variables... but I'm unsure of the application of $8\pi^2 m/h$ as it relates to mass. Apologies if this is a Modern Physics question, as I have not taken it yet. I usually have seen explanations for the rest of the function, but this part is usually considered as self-evident. I figure it's from a more elementary Physics course, but I've yet to find it's origin.
Here is the source:
$$\frac{d^2\psi}{dx^2} - \frac{8\pi^2m}{h}(E-V)\psi = 0$$ where $m$ is the mass of the particle and $V$ the expression for the potential energy. This is a one-dimensional equation, independent of time. To solve this equation one has to, first of all, define the appropriate expression for the potential energy $V$, which will depend on the problem studied. When this expression is inserted into the Schrodinger wave equation, the differential equation so obtained can be solved to find $\Psi$ and $E$. In three dimensions the Schrodinger equation becomes [...]
(From Biophysics, by V. Pattabui and N. Gautham (Kluwer, 2002).)