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Chapter 40: Q. 31 (page 1176)

Show that the normalization constantAn for the wave functions of a particle in a rigid box has the value given in Equation 40.26.

Short Answer

Expert verified

An=2L

Step by step solution

01

Given information.

We have given the one dimensional potential box.

We have to find the normalization constant of the wave function.

02

Simplify

The wave function of the particle in one dimensional box is given by,

蠄n=Ansin苍蟺虫L

then suing the normalization condition,

鈭�蠄*蠄dx=1鈭�An2sin2n蟺xL=1鈭�An2(1-cos2n蟺xL)=1An2x-sin2n蟺xL(L2n蟺)0L=1An=1L

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