Schrödinger Equation in Spherical Coordinates

[Viona]

Schrödinger Equation in Spherical Coordinates

Hello every one,

I am trying to learn how to solve three dimensional Schrödinger Equation in Spherical Coordinates. I was reading a text book and I found that there is a missed step in the solution. Please see the attached picture. It says that the solution of equation (4.25) is not simple. It gave it directly as equation (4.26). Can you help me to learn how to solve such differential equations or at least guide me to some sort of text book or lecture notes that might help.
Thank you.

 

[Deleted member 4993]

Hello every one,

I am trying to learn how to solve three dimensional Schrödinger Equation in Spherical Coordinates. I was reading a text book and I found that there is a missed step in the solution. Please see the attached picture. It says that the solution of equation (4.25) is not simple. It gave it directly as equation (4.26). Can you help me to learn how to solve such differential equations or at least guide me to some sort of text book or lecture notes that might help.
Thank you.

View attachment 10538

Do you know the nature and properties of Legendre's function? If not, then start from there.

 

[Viona]

Do you know the nature and properties of Legendre's function? If not, then start from there.

OK I will try to learn about them first. Any recommended text books?

 

[topsquark]

You should be able to find a good derivation in any Quantum Physics or Mechanics text. (I also like my Math Physics text by Arfken) By this I mean Junior to Senior year Physics classes.

-Dan