further chem
Schrödinger Equation
the hamiltonian operator can be thought of as a set of mathematical transformations to the wave function
- postulate of quantum mechanics
- comes from the emission spectrum of
solving the Schrödinger Equation gives solutions which are the atomic orbitals
- note the wave function can contain imaginary numbers
to “derive” in 3 dimensions, replace partial x with Laplacian operator (three variable function)
in quantum mechanics, physical quantities (i.e. momentum) can be replaced by quantum mechanical operators (like a composition, but can contain derivatives)
formal rigorous derivation is not possible
solving the Schrödinger Equation gives solutions which are the atomic orbitals
- note the wave function can contain imaginary numbers
the radial coordinate and angular component generates quantum numbers