Shrodinger equation

[Madelyn Romberg 1H]

What is the relationship between energy and the shrodinger equation? I do not understand the "operate a change on" part of the notes.

[Chem_Mod]

This is the Schrodinger eqution: Hψ = Eψ. Essentially, to compute this, you operate a change on ψ to yield Energy ψ. H stands for the Hamiltonian double derivative, E stands for the energy of the electron, and Ψ stands for the wave function representing the electron. The second derivative explains how Ψ appears on both sides of the equal sign (ex. the second derivative of sin is -sin: sin --> cos --> -sin). The Hamiltonian operator operates the second derivative on Ψ, or the wave function, and it results in obtaining the wave function (Ψ again, or sin again) on the right hand side of the equation.

[Daniel_Frees_1L]

I understand the overall vague idea of the Shrodinger equation, but how will it apply to our tests? What about it is important to understanding our problems if we're not going to be using the equation?