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