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Chapter 12: Q8-5P (page 562)

Find the norm of each of the following functions on the given interval and state the normalized function ${Xe}^{- X^{2}} / 2 on (0, \infty)$

Short Answer

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Concept of normalization factor

Calculate the norm of the function

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Most popular questions from this chapter

Determine the solution of the differential equations.

(a) $x y^{'}' = y$

(b) $y^{'}' - x^{4} y = 0$

To show the following equation shown in the problem

$2 \frac{d}{d x} J_{a} (x) = J_{a - 1} (x)$ .

Usingverify $(22 .19)$ and $(22.20)$ also find $L_{3} (x)$ and $L_{4} (x)$ .

Use the Section 15 recursion relations and (17.4) to obtain the following recursion relations for spherical Bessel functions. We have written them for $j_{n}$ , but they are valid for $y_{n}$ and for the $h_{n}, (\frac{d}{dx}) j_{n} (x) = {nj}_{n} (x) / x - j_{n + 1} (x) .$

Determine the raising and lowering operators for the spherical Bessel functions

$R_{n} j_{n} (x) = (\frac{n}{x} - D) j_{n} (x)$ .

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Find the norm of each of the following functions on the given interval and state the normalized function ${Xe}^{- X^{2}} / 2 on (0, \infty)$

Short Answer

Step by step solution

Concept of normalization factor

Calculate the norm of the function

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Find the norm of each of the following functions on the given interval and state the normalized functionXe-X2/2on(0,∞)

Short Answer

Step by step solution

Concept of normalization factor

Calculate the norm of the function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Medical Physics

Translational Dynamics

Atoms and Radioactivity

Engineering Physics

Electromagnetism

Radiation

Study anywhere. Anytime. Across all devices.

Find the norm of each of the following functions on the given interval and state the normalized function ${Xe}^{- X^{2}} / 2 on (0, \infty)$