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OUTLINE OF SECTION 2

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**2. **Revision: differential equations

**3. **Differential equations (cont)

**4. **Solving differential equations with exponentials

**5. **Boundary conditions

**6. **Revision: complex numbers in classical physics

**7. **An equation for matter waves: the time-dependent Schrödinger equation

**8. **An equation for matter waves (2)

**9. **An equation for matter waves (3)

**10. **The Schrödinger equation: notes

**11. **The Hamiltonian operator

**12. **Interpretation of the wave function

**13. **Example

**15. **Normalization

**17. **Conservation of probability

**18. **Boundary conditions for the wavefunction

**19. **Time-independent Schrödinger equation

**21. **SOLVING THE TIME EQUATION

**23. **Notes In one space dimension, the time-independent Schrödinger equation is an ordinary differential equation (not a partial differential equation)
The time-independent Schrödinger equation is an
eigenvalue equation for the Hamiltonian operator:
Operator × function = number × function
(Compare Matrix × vector = number × vector)
We will consistently use uppercase ?(x,t) for the full wavefunction (TDSE), and lowercase ?(x) for the spatial part of the wavefunction when time and space have been separated (TISE)

**24. **SE in three dimensions

**25. **SE in three dimensions

**26. **Puzzle