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Modern Physics
Found in: Page 413
Modern Physics

Modern Physics

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 Ψ2px and Ψ2py states of equations 101 are related to x and y just as Ψ2pz is to z.

It is proven by converting Cartesian to spherical polar coordinates.

See the step by step solution

Step by Step Solution

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 Ψ2px and Ψ2py are of the same shapes as Ψ2pz 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


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


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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