Quantum Physics - I

This problem is a little difficult version of the 1-D infinite potential problems.

If

\[ Ax(a-x) = \displaystyle\sum_{n=1}^∞ c_{n}\sqrt{\frac{2}{a}}sin(\frac{nπx}{a}) \]

where \( f(x) = Ax(a-x) , 0 ≤ x ≤ a \) is the function of a particle in a 1-D infinite potential box such that -

\[ V= 0~~ for~~ 0 ≤x ≤ a \]

\[ V = ∞ ~~for~~ -∞< x< 0~~ and~~ a < x< ∞ \]

Find \[ [1000c _{3}] \]

where \( [~~ ]\) represents the greatest integer function.

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