Conceptual Explanation of Schrod. Equ. Pls!

$H_{\psi }=E_{\psi }$

1-D: $E_{TOTAL}\psi (x)=E_{k}\psi (x)+V(x)\psi(x)=-\frac{h^{2}}{8\pi ^{2}m}\frac{d^{2}\psi(x)}{dx^{2}}+V(x)\psi(x)$

Shrita Pendekanti 4B
Posts: 22
Joined: Fri Sep 25, 2015 3:00 am

Conceptual Explanation of Schrod. Equ. Pls!

I'm having trouble understanding the verbal form of Schrodinger's Equation: "Operate a change on psi (x,y,z) = Energy psi (x,y,z)"

What does the operation of a change on an electron entail and why does it equal its energy?

Kayla Mashoudy 1B
Posts: 24
Joined: Fri Sep 25, 2015 3:00 am

Re: Conceptual Explanation of Schrod. Equ. Pls!

"Operating a change" just means taking a Hamiltonian (a double derivative in this case) of the mathematical wave function representing the position of an electron in three-dimensional space. Since electrons have wavelike properties, taking a double derivative of the wave function (using a sin or cos function) will give you the original wave function and an energy unit. For example, the derivative of sin ϑ is cos ϑ. Then, taking the derivative of cos ϑ yields -sin ϑ (ignore the negative value in this case). The actual ϑ of one of these wave functions will have units such that taking a double derivative produces units in terms of energy. These wave functions also represent orbitals (which are basically just graphical depictions of the wave functions). Overall, the Schrodinger eq. uses the wavelike properties of electrons to describe the possible energies an electron can occupy in an atom.

Hope this helps!