Superposition of spherical harmonics

[Raman Choudhary]

i am a beginner and was going through (Donald Mcquarie's "quantum chemistry" ) some discussion regarding orbitals of H-atom but i didn't get the logic behind writing px and py orbitals as linear combinations of spherical harmonics?

according to what i understood, a given spherical harmonic in itself represents a orbital depending upon n,l,m ..then how can we write a spherical harmonic as a sum of other two or spherical harmonics with same n,l.

[Mentor's note: moved from "New Member Introduction" forum to here]
[Mentor's note: title changed to be more descriptive]

 

[Raman Choudhary]

px = (1/sqrt2)*(Y11+ Y1-1)
py=(1/sqrt2*i)(Y11- Y1-1)

 

[jtbell]

Welcome to PF! This forum "New Member Introductions" is for only new member introductions and some chit-chat. Real questions belong in one of our topical forums, such as our "Quantum Physics" forum:

https://www.physicsforums.com/forums/quantum-physics.62/

Please re-post your question there. More people who can actually help you hang out there, as opposed to the few people who hang out here greeting new members.

 

[DrDu]

In hydrogen, the spherical harmonics with the same n are all energetically degenerate, so any linear combination is again a solution of the Schrödinger equation. However in molecules, the potential is perturbed and some linear combinations are better zeroth order solutions than others.