Why would one need to use the Schrodinger's wave equation? What does it give us? I understand that we solve for psi and stuff, but graphically what does it give us, in practical and not theoretical terms? What exactly is a wave function? After solving for psi with the help of the equation, we get multiple psi values. How do we know which are the "Eigen wave values"? Also, what do you even mean by a "true, meaningful"(this is how the video I watched describes Eigen wave values) psi value? Psi^2 is the probability function which tells us the probable position of the electron within the atom, why can't we just use the Heisenberg's uncertainty principle to find this instead of solving for psi using this longer, more complicated formula? Thanks in advance!