Chapter 40: Q. 31 (page 1176)

Show that the normalization constant $A_{n}$ for the wave functions of a particle in a rigid box has the value given in Equation 40.26.

Short Answer

Expert verified

$A_{n} = \sqrt{\frac{2}{L}}$

Step by step solution

Given information.

We have given the one dimensional potential box.

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

Simplify

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

$ψ_{n} = A_{n} \sin \frac{nπx}{L}$

then suing the normalization condition,

$\int ψ^{*} ψ d x = 1 \int A_{n}^{2} \sin^{2} \frac{n π x}{L} = 1 \int A_{n}^{2} (1 - \cos \frac{2 n π x}{L}) = 1 A_{n}^{2} {[x - \sin \frac{2 n π x}{L} (\frac{L}{2 n π})]}_{0}^{L} = 1 A_{n} = \sqrt{\frac{1}{L}}$

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Show that the normalization constant $A_{n}$ for the wave functions of a particle in a rigid box has the value given in Equation 40.26.

Short Answer

Step by step solution

Given information.

Simplify

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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

Step by step solution

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Simplify

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Show that the normalization constant $A_{n}$ for the wave functions of a particle in a rigid box has the value given in Equation 40.26.