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OUTLINE OF SECTION 2

Revision: differential equations. A differential equation is an equation to be satisfied by a particular function, e.g. f(x), that involves derivatives of that function, e.g. df/dx. A linear differential equation is one in which there are no powers higher than the first of the unknown function (or its derivatives)..

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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

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