# Cant understand integral tranasition to spherical coordinates

• nhrock3
In summary, the conversation discusses finding the probability in a specific region using the function Ψ = (c/√r)e-r/b. The rule is stated as the integral of the absolute value of Ψ squared over all space equaling 1. They then use spherical coordinates to simplify the integral and arrive at the final equation of b^2c^2=1.
nhrock3
there is a function $$\Psi =\frac{c}{\sqrt{r}}e^{\frac{-r}{b}}$$

find the probaility in $$\frac{b}{2}<r<\frac{3b}{2}\\$$ region

the rule states $$\int_{-\infty}^{+\infty}|\Psi|^2dv=1\\$$

$$1=\int_{-\infty}^{+\infty}|\frac{c}{\sqrt{r}}e^{\frac{-r}{b}}|^2dv$$

then they develop it as

$$c^2\int _{all space}\frac{1}{r}e^{\frac{-2r}{b}}2\pir^2dr=4\pic^2\int_{0}^{+\infty}re^{\frac{-2r}{b}}dr\\$$

they as it because of spherical coordinates

but i can't see here the jacobian of spherical coordinates.

i can't see here the x,y,z transition to r ,theta,phi

i can't see it in the last equation

Welcome to PF!

Hi nhrock3! Welcome to PF!

(have a pi: π and an infinity: ∞ and an integral: ∫ and try using the X2 and X2 tags just above the Reply box )

I'm a little confused by what you've written, but basically you start with

∫ c2/r e-2r/b dxdydz

and because it's spherically symmetric, you can divide the region into spherical shells of radius r and volume 4πr2dr,

which gives you ∫0 c2/r e-2r/b 4πr2dr

= 4πc20 r e-2r/b dr

## What are spherical coordinates?

Spherical coordinates are a three-dimensional coordinate system used to locate points in space. They consist of a distance from the origin (r), an angle in the xy-plane (θ), and an angle from the z-axis (φ).

## Why is it important to understand integral transition to spherical coordinates?

Understanding integral transition to spherical coordinates allows us to solve problems involving three-dimensional objects, such as spheres or cones, more efficiently. It also helps us visualize and analyze complex systems in physics and engineering.

## What is the process of transitioning to spherical coordinates?

The process of transitioning to spherical coordinates involves converting the Cartesian coordinates (x, y, z) of a point to its corresponding spherical coordinates (r, θ, φ). This can be done using mathematical equations and trigonometric functions.

## What are some common applications of spherical coordinates?

Spherical coordinates are commonly used in fields such as astronomy, physics, and engineering to describe the position and motion of objects in three-dimensional space. They are also used in computer graphics and 3D modeling to create realistic images and animations.

## How can I improve my understanding of integral transition to spherical coordinates?

To improve your understanding, you can practice solving problems involving spherical coordinates, watch tutorials or attend lectures on the topic, and consult with experts or colleagues for clarification. It may also be helpful to review your knowledge of trigonometry and basic calculus.

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