Schrodinger's Wave Function Equation [ENDORSED]

[Ryan Neis 2L]

I'm just confused as to what this equation exactly tells us? What does it mean when it says it finds the height of a wave at position x, y, z?

[Chem_Mod]

The Schrodinger equation can't be derived from basic principles. It is a differential equation that, in terms of its mathematical origins, is beyond the scope of the course. However, you should understand that when given a certain "wavefunction," the Schrodinger equation, in its simplest form, will produce the energy of that wavefunction. This wavefunction can be any suitable function that obeys the criteria:

1. It must be "smooth." That is, the function must be continuous and all its partial derivatives must be continuous.

2. It must be quadratically integrable.

3. It must be single valued.

4. The wavefunctions must form an orthonormal set.

5. The wavefunction must be finite everywhere.

6. The wavefunction must obey the boundary conditions of the system is represents.

Again, this is beyond the requirements of the course. The meaning of "height of a wave at x,y,z" simply means that the Schrodinger equation predicts the wavefunction's shape.