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I am not aware of any analogous approximation formula for more than two turning points (maybe someone out there does), and would risk saying that you would have to explicitly work out the WKB-approximate wave function as well as the connection formulas. The reference I can recommend for a nice introduction to the subject would be David J. Griffiths' ...


I was also involved in this problem for the past few weeks.You can write newtons law of motion for small segment of string and obtain a differential equation.From that equation you can find the normal modes of the string and the general motion of the string is given by a superposition of the normal modes.But i ignored the longitudinal oscillations and ...


In my 1995 edition the text (on page 242) reads: So presumably this is an error in whatever edition you have.

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