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Unformatted text preview: ) (4.12) In region II we have the oscillatory solution (4.13) Now we have to impose the conditions on the wave functions we have discussed before, continuity of and its derivatives. Actually we also have to impose normalisability, which means that (exponentially growing functions can not be normalised). As we shall see we only have solutions at certain energies. Continuity implies that (4.14) Tactical approach: We wish to find a relation between and (why?), removing as manby of the constants and . The trick is to first find an equation that only contains and . To this end we take the ratio of the first and third and second and fourth equation: (4.15) We can combine these two equations to a single one by equating the righthand sides. After deleting the common factor , and multiplying with the denominators we find (4.16) which simplifies to (4.17) We thus have two families of solutions, those characterised by and those that have ....
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 Fall '10
 DavidJudd
 Physics, Derivative, ORDINARY DIFFERENTIAL EQUATIONS, exponentially growing functions

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