# How can I deform electron orbitals?

• DmplnJeff

#### DmplnJeff

It's my understanding that electron orbitals arise from the steady state solution to the Schrodinger equation. In what ways can these be deformed?

Some possible solutions might be oscillating or metastable dynamic solutions. Other solutions include varying electron mass (I understand a purist might consider muons to be separate case, but I'm interested in a broader view of what's possible.)

Is there a book or perhaps some cheap visualization software I could study? Are there any weird solutions I might otherwise miss?

No responses?

Is my understanding flawed? Was this a stupid question? Is this a bad way to look at electron orbitals? Is this in the wrong forum?

Any feedback would be appreciated.

In what context did you hear about deformation?
It is not a too fundamental concept. Orbitals are a solution of a one-particle Schroedinger equation. Now if you change the potential in the Hamiltonian, also the corresponding solutions will change or "deform".

I didn't hear about them (except muons changing the interatomic distances in room temperature fusion). I assumed they exist from the math.

The orbital derivation I saw started by assuming a static situation to make the math easier (and because atoms are static as a rule). But if one is willing to provide for different initial conditions, the outcome will be different.

If I understand your question right, one common way of deforming the orbitals is to put them into a time-varying Hamiltonian, for instance by introducing an oscillating electric field. This can induce transitions from one orbital to another, and is the way that standard QM calculates things like photon emission/absorption. These sorts of problems are solved with time-dependent perturbation theory.

As far as visualizing them goes, http://www.falstad.com/mathphysics.html" [Broken] contains a bunch of really neat Java apps that demonstrate some of the basic principles behind QM. You might try checking out the "Atomic Dipole Transitions" app for this specific question (although all of them are pretty fun to play with.)

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Thank you both for taking the time to answer.

Chopin, I'll look into time dependent perturbation theory. Thanks for the visualization link as well. I suspect it will provide hours of fun deciding what all the colors and axis mean.

Er... what about bringing another atom nearby? That's what hybridization is all about!

Zz.