PCh10 Lec 3
(4/29/20, bes)
Well...we are making great progress in the material. Great job turing in your lab reports!
Let's take a step back and look at the big picture...we have come a long way...
The Big Picture
As stated on the Wikipedia site, the time-independent Schrodinger equation looks like the following:
- YES...sorry this is considered the easier, time-independent Schrodinger equation...the time-dependent Schrodinger equation is used in spectroscopy since there is a time-dependence of when you excite the system...it apply a pulse of RF in FT-NMR...or any light (UV, vis, IR, etc). Time-dependent quantum or "Quantum: Spectroscopy" is a graduate level class that most pchem PhD students will take.
Parts of Schrodinger Equation
As we transition from the analytical solutions for the model QM systems and H-atom (Ch < 10) to the numerical solutions for the real-world chemical systems (Ch > 10), we can separate our discussions based on the 3 (interconnected) aspects of a the Schrodinger equation. I will outline these discussion below and then go into more details later.
Hamiltonian
Wavefunctions
Calculation of Energy
Sec 10.4: Using the Variational method to solve the Schrodinger equation.
- As the name states the "variational method" means that you very some parameter in the Schrodinger equation and then calculate the energy. This method introduces some vocabulary...to start this method we select a "trial wavefunction".