# Schrödinger wave equation - mass component

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).)

Serious QM texts will generally present the Schrödinger equation in the form $$-\frac{\hbar^2}{2m}\frac{d^2\psi}{dx^2} +(V-E)\psi = 0,$$ where the factor of $$-\frac{\hbar^2}{2m}\frac{d^2}{dx^2}\psi$$ acting on the wavefunction comes from the kinetic-energy term $$\frac{\hat{p}^2}{2m}\psi$$ and the identification $$\hat p = -i\hbar \frac{d}{dx}$$. (For more information on those, see any serious QM textbook.)
• expand the reduced Planck's constant as $$\hbar = h/2\pi$$ explicitly (despite the fact that no serious physics treatment this side of the 1950s will do that),
• get the denominator wrong by skipping the missing square in front of the $$h$$.
If you do want to write the Schrödinger equation in that form, then the correct way to write it is $$\frac{d^2\psi}{dx^2} + \frac{8\pi^2m}{h^2}(E-V)\psi = 0.$$ Though if you really want to learn QM, I would recommend looking for an alternative resource - none of the above inspires me with any confidence in that text.