How Do You Solve the Schrödinger Equation Using Polar Coordinates?

[KingBigness]

Homework Statement

See attached photo

Homework Equations

none

The Attempt at a Solution

Just hoping someone could give me a hand with this.

I think I need to convert polar coords into y and z using trig then perform an addition of the wavefunctions as the linear transform says, finally using the Euler's formulae to simplify the exponentials resulting in the answer...I'm just not a hundred percent sure on how to do it. Any help would be awesome.

 

[vela]

I'd do it in the opposite order. Add the wave functions first and simplify. Then convert to Cartesian coordinates.

In any case, even though you may not see how it's going to work out already, just start chugging away on it. It should become clear as you work on it.

 

[kuruman]

First, just take the linear combination that the problem suggests. Then see if you can identify y and z (in polar form) in your expression.

 

[KingBigness]

thanks for the replies...bit late now so Ill do it in the morning, btu can you refresh me on how the take the linear

 

[vela]

Do you understand what the problem means by the notation d₊₁ and d_-1?

 

[mathfeel]

Do you understand what the problem means by the notation d₊₁ and d_-1?

d orbital means l = 2.
+1 and -1 are values of m.

 

[vela]

I know you know. I want to know if KingBigness knows.

 

[KingBigness]

I know you know. I want to know if KingBigness knows.

Yes I see that and I understand most of it I just can't figure out where it all fits... guess that means I don't understand it haha

Just not sure how to use a linear combination...I'm sure it is something easy and I'll feel like an idiot when I see the answer but right now I just don't

 

[vela]

Just plug the functions into that expression and simplify. I'm not sure any of us sees where you're getting confused (and we won't until we can see your stab at solving the problem).

 

[KingBigness]

Thanks for all your help woke up this morning has a stab and got it. Felt like and idiot after I solved it! Haha
Sorry for all the confusion just wasn't thinking straight.
Thanks again for all your help