Book edition 2nd Edition

Author(s) Randy Harris

Pages 633 pages

ISBN 9780805303087

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Short Answer

Upon what definitions do we base the claim that the $Ψ_{2 p x}$ and $Ψ_{2 p y}$ states of equations $(10 - 1)$ are related to x and y just as $Ψ_{2 p z}$ is to $z$ .

It is proven by converting Cartesian to spherical polar coordinates.

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TABLE OF CONTENTS :

TABLE OF CONTENTS

A concept of polar coordinate

A polar coordinate is one of two numbers that identify a point in a plane based on its distance from a fixed point on a line and the angle that line makes with the fixed line.

Understanding the Similarities and Differences between these Wave Functions

States $Ψ_{2 p x}$ and $Ψ_{2 p y}$ are of the same shapes as $Ψ_{2 p z}$ and they are all equivalent. The only difference between these states is the orientation of coordinates. These wave functions are defined based on spherical polar coordinates. $(γ, θ, ϕ)$ .

Transformation of Coordinates

The transformation between Cartesian and spherical polar coordinates is

$\begin{array}{l} x = r \sin θ \cos θ \\ y = r \sin θ \cos θ \\ z = r \cos θ \end{array}$

The wave functions of the 2px, 2py and 2pz states are given as

$\begin{array}{l} Ψ (x) = Ψ_{2 p x} a \sin θ \cos θ \\ Ψ (y) = Ψ_{2 p y} a \sin θ \cos θ \\ Ψ (z) = Ψ_{2 p z} a \cos θ \end{array}$

Hence, from this its prove that the states 2px, 2py and 2pz depends on angles $θ$ and $ϕ$ which are the same as that described in Cartesian coordinates for X, Y, and Z .

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Modern Physics

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Short Answer

Upon what definitions do we base the claim that the $Ψ_{2 p x}$ and $Ψ_{2 p y}$ states of equations $(10 - 1)$ are related to x and y just as $Ψ_{2 p z}$ is to $z$ .

Step by Step Solution

A concept of polar coordinate

Understanding the Similarities and Differences between these Wave Functions

Transformation of Coordinates

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Modern Physics

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Short Answer

Upon what definitions do we base the claim that the Ψ2px and Ψ2py states of equations 10−1 are related to x and y just as Ψ2pz is to z.

Step by Step Solution

A concept of polar coordinate

Understanding the Similarities and Differences between these Wave Functions

Transformation of Coordinates

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Upon what definitions do we base the claim that the $Ψ_{2 p x}$ and $Ψ_{2 p y}$ states of equations $(10 - 1)$ are related to x and y just as $Ψ_{2 p z}$ is to $z$ .