3. Variational Method Variational Principle
Depends on variational parameters
The more we use:
The more complicated the function
The closer we get to the true value
the lowest eigenvalue of an arbitrary wavefunction is greater than or equal to the minimum
Variational Method
Proof:

4. Hydrogen Example

5. Hydrogen Example S-orbital & guess function, 
s-orbital &  with more variables

6. Helium Example

8. Secular Determinants Getting all the players in order
VM & Linear Combos of Functions
We work our way into a matrix representation
& solve the system with determinants
Secular Determinants
The Generalized Case

9. Simplified N=2 Example

10. Matrices & Determinants
where we solve
Matrices & Determinants

11. Applied to 1D PIB Overall nice fit (better than average)
The root is an approximation for 1st e.s.

13. Used to Solve for Excited States

14. Perturbation Theory The Setup Applied Example
Use perturbation theory to calculate the first - order
correction to the ground-state energy of a quartic
oscillator whose
Use Harmonic Oscillator for the unperturbed system.

16. SKIP