Campuses:
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| - | ===== Sept 21 (Mon) ===== | + | ===== Sept 21 (Mon) Raising/ |
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| === Main Points === | === Main Points === | ||
| - | *Special Functions | + | |
| - | *Raising/ | + | |
| - | *Structuring DEs | + | |
| - | *Expectation of Momentum / Momentum Squared | + | |
| - | *Orthogonality of Hermitian Operators | + | |
| - | *Introduction to the Analytical Method (next lecture) | + | |
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| == Special Functions == | == Special Functions == | ||
| - | One of the first points made today was that special functions such as the Bessel Functions, Legendre Polynomials and Hermite Polynomials keep emerging as solutions to various classes of differential equations. The important aspect of this fact is that when one function of a class is a solution, usually other functions in that class and sometimes linear combinations of the functions are solutions as well. One of the most familiar examples is the types of differential equations we commonly see as physics students: < | + | One of the first points made today was that special functions such as the Bessel Functions, Legendre Polynomials and Hermite Polynomials keep emerging as solutions to various classes of differential equations. The important aspect of this fact is that when one function of a class is a solution, usually other functions in that class and sometimes linear combinations of the functions are solutions as well. One of the most familiar examples is the types of differential equations we commonly see as physics students: < |